nT3 One-D Motion 8-21-#27AA - School District of Clayton Field Test version © nTIPERs nT3 1-D...

1/33 Field Test version © nTIPERs nT3 1-D Motion 8-21-08

nT3 Motion in One Dimension 8-21-08

NT3 MOTION IN ONE DIMENSION TOPICS OUTLINEA Motion graphs in one dimension (piece-wise continuous)B Average velocity in one dimensionC Instantaneous velocity in one dimensionD Average acceleration in one dimensionE Instantaneous acceleration in one dimensionF Velocity graphs in 1-D as a function of constant accelerationG Position graphs in 1-D as a function of constant acceleration

nT3 Motion in One Dimension Topics Outline ...................................................................................... 1nT3A-WWT1: Velocity vs. Time Graph I—Acceleration vs. Time Graph ............................................ 2nT3A-WWT2: Velocity vs. Time Graph II—Acceleration vs. Time Graph ........................................... 3nT3A-WWT3: Acceleration vs. Time Graph—Velocity vs. Time Graph............................................... 4nT3A-WWT4: Velocity vs. Time Graph—Acceleration vs. Time Graph............................................... 5nT3A-CRT1: Acceleration vs. Time Graph—Velocity vs. Time Graph................................................. 6nT3A-CRT2: Velocity vs. Time Graph—Acceleration vs. Time Graph................................................. 7nT3A-CT1: Velocity vs. Time Graphs of Two Objects I— Displacement ............................................. 8nT3A-CT2: Velocity vs. Time Graphs of Two Objects II—Displacement ............................................. 9nT3A-RT1: Velocity vs. Time Graphs—Displacement ........................................................................ 10nT3A-WWT5: Ball Thrown Upward and Comes Back Down—Velocity vs Time Graph ................... 11nT3A-WWT6: Velocity vs Time Graph of Two Objects—Fastest Object ........................................... 12nT3A-CRT3: Traveling Carmela and Desi—Velocity vs Time Graph ................................................. 13nT3A-CCT1: Velocity vs. Time Graph—Displacement....................................................................... 14nT3A-BCT1: Velocity vs. Time Graph—Displacement....................................................................... 15nT3A-CT3: Velocity vs. Time Graphs—Displacement ........................................................................ 16nT3A-RT2: Velocity vs. Time Graphs—Distance Traveled................................................................. 17nT3A-BCT2: Velocity vs. Time Graph—Distance Traveled................................................................ 18nT3B-WBT1: Kinematic Equation—Physical Situation....................................................................... 19nT3B-WBT2: Kinematic Equation—Physical Situation....................................................................... 20nT3C-RT1: Position as a Function of Time Equations—Instantaneous Speed ..................................... 21nT3C-RT2: Position Along a Line as a Function of Time Equations—Velocity .................................. 22nT3C-RT4: Velocity Versus Time Graphs—Instantaneous Velocity ................................................... 23nT3C-RT5: Velocity Versus Time Graphs—Acceleration ................................................................... 24nT3C-RT6: Position Versus Time Graphs—Instantaneous Speed........................................................ 25nT3C-RT7: Position Versus Time Graphs—Displacement .................................................................. 26nT3C-RT3: Position Versus Time Graphs—Instantaneous Velocity.................................................... 27nT3F-RT1: Velocity vs. Time Graphs—Displacement of Identical Objects......................................... 28nT3F-RT2: Velocity vs. Time Graphs—Average Velocity of Identical Objects .................................. 29nT3F-RT3: Velocity vs. Time Graphs—Acceleration of Identical Objects .......................................... 30nT3F-RT4: Velocity vs. Time Graphs—Acceleration of Objects ......................................................... 31nT3G-RT1: Position vs. Time Graph—Acceleration............................................................................ 32nT3G-QRT1: Position Versus Time Graphs—Acceleration and Velocity............................................ 33

2/33 Alpha version © nTIPERs nT3 1-D Motion 7-9-08

NT3A-WWT1: VELOCITY VS. TIME GRAPH I—ACCELERATION VS. TIME GRAPHA student has obtained a graph of an object’s velocity versus time and then draws the graph of theacceleration versus time for the same time interval.

v

time

a

time

What, if anything, is wrong with the graph of the acceleration versus time? If something iswrong, identify it and explain how to correct it.

Answer- the second set of peaks (# 3 and 4) should be reversed as shown below-


NT3A-WWT2: VELOCITY VS. TIME GRAPH II—ACCELERATION VS. TIME GRAPHA student has obtained a graph of an object’s velocity versus time and then draws the graph of theacceleration versus time for the same time interval.

v

time

a

time


Answer- the peaks # 2 and #4 should be reversed as shown below to bring the velocity back to zero-


NT3A-WWT3: ACCELERATION VS. TIME GRAPH—VELOCITY VS. TIME GRAPHA student has obtained a graph of an object’s acceleration versus time and then draws the graph of thevelocity versus time for same the time interval.

v

time

a

time

What, if anything, is wrong with the graph of velocity versus time? If something is wrong,identify it and explain how to correct it.

Answer-the change in velocity is related to the area under the acceleration vs time graphThus the velocity graph should be something like-


NT3A-WWT4: VELOCITY VS. TIME GRAPH—ACCELERATION VS. TIME GRAPHA student has obtained a graph of an object’s velocity versus time and then draws the graph of theacceleration versus time for the same time interval.

v

time

a

time


Answer-the change in velocity related to the area under the graph of acceleration vs. time or theacceleration is related to the slope of the velocity graph-so we need to adjust the acceleration graphto bring the velocity back to the original value. Changing the acceleration graph gives this:


NT3A-CRT1: ACCELERATION VS. TIME GRAPH—VELOCITY VS. TIME GRAPH

Sketch a possible velocity versus time graph given the acceleration graph for the same timeinterval. Explain.

a

time

v

time

Answer-the change in the velocity is related to the area under the acceleration graph. The second blip isdeeper than the first so it contains more area.


NT3A-CRT2: VELOCITY VS. TIME GRAPH—ACCELERATION VS. TIME GRAPH

Sketch the acceleration versus time graph given the velocity versus time graph for the same timeinterval. Explain.

v

time

a

time

Answer-the acceleration is the slope of the velocity graph thus


NT3A-CT1: VELOCITY VS. TIME GRAPHS OF TWO OBJECTS I— DISPLACEMENTThe graphs below show the velocity of two objects during the same time interval.

v1

time64200

1

2

v2

time64200

1

2

Object 2

Object 1

After five seconds, is the displacement of object 1 in the top graph (a) greater than, (b) equal to,or (c) less than the displacement of object 2 in the bottom graph?Explain.

Answer-less than, object 2 has a larger displacement since the displacement is equal to the area underthe graph of velocity vs. time and the area is larger for object 2.


NT3A-CT2: VELOCITY VS. TIME GRAPHS OF TWO OBJECTS II—DISPLACEMENTThe graphs below show the velocity of two objects during the same time interval.

v1

time64200

1

2

v2

time64200

1

2

Object 2

Object 1

After five seconds, is the displacement of object one in the upper graph (a) greater than, (b) equalto, or (c) less than the displacement of object two in the lower graph?Explain.

Answer-Greater for object one since the displacement is equal to the area under the graph of velocity vs.time.


NT3A-RT1: VELOCITY VS. TIME GRAPHS—DisplacementShown below are six velocity-time graphs for toy robots that are traveling along a straight course. Allthe robots are initially facing the same way. All graphs for the robots have the same time and velocityscales.

A B C

D E F

Velocity Velocity

Time

Velocity

Time

Velocity

Time

Velocity

Time

Velocity

Time

Time

Rank these situations from greatest to least on the basis of the displacement during theseintervals (positives rank higher than negatives).

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The displacements during the intervals indicated are the same for ALL SIX robots ___

OR, The displacements during the intervals indicated are zero for ALL SIX robots. ___

OR, We cannot determine the ranking for the displacements of these robots. ___

Please explain carefully your reasoning.

Answer: D > B > F > E > C > A; the displacements are given by the areas under the graphs.


NT3A-WWT5: BALL THROWN UPWARD AND COMES BACK DOWN—VELOCITY VS TIME GRAPHA ball is thrown straight upward and falls back to the same height. A student makes the followinggraph of the velocity of the ball as a function of time:

Velocity, m/s

Time, s

What, if anything, is wrong with the student’s graph? If something is wrong, explain the errorand how to correct it. If the graph is correct, explain why.

The line should go across the axis and continue in a straight line into the negative region since thevelocity is negative on the way back down,


NT3A-WWT6: VELOCITY VS TIME GRAPH OF TWO OBJECTS—FASTEST OBJECTA student is shown the velocity-time graphs for two objects below and is asked to decide whichobject is faster. The student responds:

Velocity, m/s

Time, s

A

B

“B is faster because it has the larger slope.”

What, if anything, is wrong with the student’s statement? If something is wrong, explain theerror and how to correct it. If the statement is correct, explain why.

Answer: A is faster because it is above B at every point shown on the graph. The slope is related to theacceleration and B has the larger acceleration because it has the larger slope.


NT3A-CRT3: TRAVELING CARMELA AND DESI—VELOCITY VS TIME GRAPHCarmela and Desi leave their physics classroom separately and travel west. They both start from rest.Desi leaves first traveling with an acceleration of 4 m/s

2 west for the first 6 seconds and then he

travels at a constant velocity. Two seconds after Desi started, Carmela begins with an acceleration of3 m/s

2 west for 10 seconds and after that she travels at a constant velocity.

Graph the velocity of both travelers as a function of time up to t = 16 seconds and let time t = 0when Desi leaves. Use a solid line for Desi’s velocity and a dashed line for Carmela’s velocity.

Velocity, m/s

Time, s

10

20

30

40

00 2 4 6 8 10 12 14 16

Answer-


NT3A-CCT1: VELOCITY VS. TIME GRAPH—DisplacementThe graph represents the velocity of a toy robot for a particular time interval.

Velocity, m/s

Time, s

Three students studying this graph make the following statements:

Arnold: “The robot’s displacement is positive because the slope of the graph is positive.”

Betty: “No, the robot’s displacement will be zero since it moves in both the positive and negativedirections during this time.”

Cindy: “I think the displacement is negative since the robot has a negative velocity for a longertime.”

Which, if any, of these three students do you agree with and think is correct?

Arnold _____ Betty _____ Cindy _____ None of them______


Cindy is correct but her reasoning could be more complete. The displacement can be found from thearea between the time axis and the velocity-time graph. For the time interval shown, the robotmoves in the negative direction until the graph crosses the axis, and the displacement in thisdirection is equal to the area of the triangle bounded by the two axes and the line representing therobot’s velocity. This area is larger than the area of the triangle above the time axis representing therobot’s displacement in the positive direction up to the end of this time interval, so there is anoverall displacement in the negative direction.


NT3A-BCT1: VELOCITY VS. TIME GRAPH—DisplacementThe graph represents the motion of a toy robot during a 14 second interval.

Velocity, m/s

Time, s

–2

–4

2

4

02 4 6 8 10 12 14 16

Below is a bar graph for the displacement of the robot during two-second intervals with thedisplacement from 10 s to 12 s completed.

0 – 2 s 2 – 4 s 4 – 6 s 6 – 8 s 8 – 10 s 10 – 12 s

– 2 m

– 4 m

– 6 m

2 m

4 m

6 m

0

Displacement during interval

12 – 14 s

Complete the bar charts for the other two-second intervals.Answer


NT3A-CT3: VELOCITY VS. TIME GRAPHS—DisplacementThe graphs represent the velocity of two toy robots for a particular time interval. Both graphs havethe same time and velocity scales.

Case A

Time

Velocity

Case B

Time

Velocity

Is the magnitude of the displacement of the robot in Case A greater than, less than, or equal tothe magnitude of the displacement of the robot in Case B?Please explain carefully your reasoning.

The displacement is the area between the velocity-time curve and the time axis. The displacement inCase A is zero while the displacement for case B is negative. The magnitude of the displacement isgreater in case B.


NT3A-RT2: VELOCITY VS. TIME GRAPHS—Distance TraveledVelocity-time graphs for six toy robots that are traveling along a straight course are shown. All therobots are initially facing in the same direction. All graphs for the robots have the same time andvelocity scales.

A B C

D E F

Velocity Velocity

Time

Velocity

Time

Velocity

Time

Velocity

Time

Velocity

Time

Time

Rank these situations from greatest to least on the basis of the distance traveled during theseintervals.

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The distances during the intervals indicated are the same for ALL SIX robots. ___

OR, The distances during the intervals indicated are zero for ALL SIX robots. ___

OR, We cannot determine the ranking for the distances traveled of these robots. ___

Please explain carefully your reasoning.D > A > B = C > E = F, add up areas under the lines without concern for signs.


NT3A-BCT2: VELOCITY VS. TIME GRAPH—Distance TraveledThe graph represents the motion of a toy robot during a 14-second interval.

Velocity, m/s

Time, s

–2

–4

2

4

02 4 6 8 10 12 14 16

In the histogram below, the bar represents the distance the robot travels during the two-secondinterval from 4 s to 6 s.

0 – 2 s 2 – 4 s 4 – 6 s 6 – 8 s 8 – 10 s 10 – 12 s

2 m

4 m

6 m

0

Distance traveled during interval

12 – 14 s

8 m

Draw additional bars to represent the distance traveled during the other two-second intervals.


NT3B-WBT1: KINEMATIC EQUATION—Physical SituationAn object moves along a horizontal surface in a manner described by the kinematic equation below:

Xf = 38 m – (2.8 m/s)(14 s)

Draw a physical situation that would result in this equation. Explain how your drawing isconsistent with the equation.

Answer:This object began 38 m away from the chosen origin and traveled at a constant velocity of 2.8 m/s in the

negative direction towards the origin for 14 seconds, ultimately traveling 39.2 m passing the originending up 1.9 m on the other side of it.


NT3B-WBT2: KINEMATIC EQUATION—Physical SituationAn object moving along a horizontal surface during two consecutive intervals is described by thesetwo kinematic equations:

x1 = -4 m/s(1.53 s) + (0.5)(a)(1.53 s)2

4.9 m = x1 + (0.5)(a)(2.47 s)2

Solve for a and x1, and then draw a physical situation that would be described by theseequations. Explain how your drawing is consistent with the equations.

Answer: The object slows down at a constant acceleration, stops at an instant and then continues toaccelerate at the same rate in the direction opposite to which it was initially moving.


NT3C-RT1: POSITION AS A FUNCTION OF TIME EQUATIONS—Instantaneous SpeedThe six equations below tell us the position in meters as a function of time in seconds for six objectsthat are moving along a straight line. As the equations show, these objects vary in their initialpositions, initial velocities, and accelerations.

A.

€

x(t) = −7 + 9t − 2t 2 B.

€

x(t) = +4 + 9t + t 2 C.

€

x(t) = +3− 7t − 2t 2

D.

€

x(t) = −4 + 3t − 4t 2 E.

€

x(t) = −1− 9t − 2t 2 F.

€

x(t) = −7 + t + 2t 2

Rank these situations from greatest to least on the basis of the speed of the objects 2 secondsafter their motions begin.

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The speeds at 2 seconds are the same but not zero for ALL SIX objects. ___

OR, The speeds at 2 seconds are zero for ALL SIX objects. ___

OR, We cannot determine the ranking for the speeds of these objects. ___


Answer: E>C>B=D>F>A based on taking a derivative, substituting 2 seconds for the time, and rankingthe absolute values.


NT3C-RT2: POSITION ALONG A LINE AS A FUNCTION OF TIME EQUATIONS—VelocityThe six equations below tell us the position in meters as a function of time in seconds for six objectsthat are moving along a straight line. As the equations show, these objects vary in their initialpositions, initial velocities, and accelerations.

A.

€

x(t) = −7 + 9t − 2t 2 B.

€

x(t) = +4 + 9t + t 2 C.

€

x(t) = +3− 7t − 2t 2

D.

€

x(t) = −4 + 3t − 4t 2 E.

€

x(t) = −1− 9t − 2t 2 F.

€

x(t) = −7 + t + 2t 2

Rank these situations from greatest to least on the basis of the velocities of the objects 2 secondsafter their motions begin (positives rank higher than negatives).

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The velocities at 2 seconds are the same but not zero for ALL SIX objects. ___

OR, The velocities at 2 seconds are zero for ALL SIX objects. ___

OR, We cannot determine the ranking for the velocities of these objects. ___


Answer: B>F>A>D>C>E based on taking a derivative, substituting 2 seconds for the time and rankingthe values.


NT3C-RT4: VELOCITY VERSUS TIME GRAPHS—Instantaneous VelocityThe graphs below show the velocity versus time for six sailboats traversing a long narrow channelthat runs east to west. The scales on both axes are the same for all six graphs and east is on the upperpart of the position axis. In each graph a point is marked with a dot.

Velocity

Time

A Velocity

Time

B Velocity

Time

C

Velocity

Time

EVelocity

Time

D Velocity

Time

F

Rank these situations from greatest to least on the eastward velocity of the sailboat at the pointindicated.

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The velocities at the points indicated are the same for ALL SIX boats. ___

OR, The velocities at the points indicated are zero for ALL SIX boats. ___

OR, We cannot determine the ranking for the velocities of these boats. ___


Answer: F>B>A=C>E>D; the instantaneous velocities are determined by the position on the graphs.


NT3C-RT5: VELOCITY VERSUS TIME GRAPHS—AccelerationThe graphs below show the velocity versus time for six sailboats traversing a long narrow channelthat runs east to west. The scales on both axes are the same for all six graphs and east is on the upperpart of the position axis. In each graph a point is marked with a dot.

Velocity

Time

A Velocity

Time

B Velocity

Time

C

Velocity

Time

EVelocity

Time

D Velocity

Time

F

Rank these situations from greatest to least on the eastward acceleration of the sailboat at thepoint indicated.Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The accelerations at the points indicated are the same for ALL SIX boats. ___

OR, The accelerations at the points indicated are zero for ALL SIX boats. ___

OR, We cannot determine the ranking for the accelerations of these boats. ___


Answer: A=B>E>F>C=D; the instantaneous accelerations are determined by the slopes at the points onthe graphs.


NT3C-RT6: POSITION VERSUS TIME GRAPHS—Instantaneous SpeedThe graphs below show the position versus time for six sailboats traversing a long narrow channel.The scales on both axes are the same for all six graphs. In each graph a point is marked with a dot.

Position

Time

A Position

Time

B Position

Time

C

Position

Time

EPosition

Time

D Position

Time

F

Rank these situations from greatest to least on the basis of the speed of the sailboat at the pointindicated.Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The speeds at the points indicated are the same for ALL SIX boats. ___

OR, The speeds at the points indicated are zero for ALL SIX boats. ___

OR, We cannot determine the ranking for the speeds of these boats. ___


Answer: C = D > A = B > E = F; the instantaneous speeds are determined by the magnitudes of theslopes.


NT3C-RT7: POSITION VERSUS TIME GRAPHS—DisplacementThe graphs below show the position versus time for six sailboats traversing a long narrow channelthat runs east to west. The scales on both axes are the same for all six graphs. In each graph twopoints are marked with dots.

Position

Time

A Position

Time

B Position

Time

C

Position

Time

D Position

Time

E Position

Time

F

Rank these situations from greatest to least on the basis of the displacement between the twopoints (positives rank higher than negatives).Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The displacements between the points indicated are the same for ALL SIX boats ___

OR, The displacements between the points indicated are zero for ALL SIX boats. ___

OR, We cannot determine the ranking for the displacements of these boats. ___


Answer: B > A > E > F > D > C; the magnitudes of the displacements can be read as the distancebetween the positions on the vertical axes fro the two points.


NT3C-RT3: POSITION VERSUS TIME GRAPHS—Instantaneous VelocityThe graphs below show the position versus time for six sailboats traversing a long narrow channelthat runs east to west. The scales on both axes are the same for all six graphs and east is on the upperpart of the position axis. In each graph a point is marked with a dot.

Position

Time

A Position

Time

B Position

Time

C

Position

Time

EPosition

Time

D Position

Time

F

Rank these situations from greatest to least on the basis of the eastward velocity of the sailboatat the point indicated.Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The eastward velocities at the points indicated are the same for ALL SIX boats ___

OR, The eastward velocities at the points indicated are zero for ALL SIX boats. ___

OR, We cannot determine the ranking for the eastward velocities of these boats. ___


Answer: A = B > E > F > C = D; the instantaneous velocities are determined by the slopes.


NT3F-RT1: VELOCITY VS. TIME GRAPHS—DISPLACEMENT OF IDENTICAL OBJECTSShown below are graphs of velocity versus time for four seconds for six identical objects that movealong a straight, horizontal surface under the action of a force exerted by an external agent.

2 s

A

4 s0

+2 m/s

–2 m/s

2 s

B

4 s0

+2 m/s

–2 m/s

2 s

C

4 s0

+2 m/s

–2 m/s

2 s

D

4 s0

+2 m/s

–2 m/s

2 s

E

4 s0

+2 m/s

–2 m/s

2 s

F

4 s0

+2 m/s

–2 m/s

Rank these situations from greatest to least on the basis of the displacement of the objects duringeach of these intervals (positives rank higher than negatives).Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The displacement is the same for ALL SIX situations. ___

OR, The displacement is zero for ALL SIX situations. ___

OR, We cannot determine the ranking for the displacement for these situations. ___


Answer: A=E > C = D =F > BThe displacement is equal to the positive or negative area under the graphs of velocity vs time.


NT3F-RT2: VELOCITY VS. TIME GRAPHS—AVERAGE VELOCITY OF IDENTICAL OBJECTSShown below are graphs of velocity versus time for four seconds for six identical objects that movealong a straight, horizontal surface under the action of a force exerted by an external agent.

2 s

A

4 s0

+2 m/s

–2 m/s

2 s

B

4 s0

+2 m/s

–2 m/s

2 s

C

4 s0

+2 m/s

–2 m/s

2 s

D

4 s0

+2 m/s

–2 m/s

2 s

E

4 s0

+2 m/s

–2 m/s

2 s

F

4 s0

+2 m/s

–2 m/s

Rank these situations from greatest to least on the basis of the average velocity of the objects duringeach of these intervals (positives rank higher than negatives).Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The average velocity is the same for ALL SIX situations. ___

OR, The average velocity is zero for ALL SIX situations. ___

OR, We cannot determine the ranking for the average velocity for these situations. ___


Answer: A=E > C = D =F > BThe average velocity is equal to the displacement of the object divided by the time interval of the

displacement. Since the time intervals are the same, it has the same ranking as the displacement.


NT3F-RT3: VELOCITY VS. TIME GRAPHS—ACCELERATION OF IDENTICAL OBJECTSShown below are graphs of velocity versus time for four seconds for six identical objects that movealong a straight, horizontal surface under the action of a force exerted by an external agent.

2 s

A

4 s0

+2 m/s

–2 m/s

2 s

B

4 s0

+2 m/s

–2 m/s

2 s

C

4 s0

+2 m/s

–2 m/s

2 s

D

4 s0

+2 m/s

–2 m/s

2 s

E

4 s0

+2 m/s

–2 m/s

2 s

F

4 s0

+2 m/s

–2 m/s

Rank these situations from greatest to least on the basis of the acceleration of these objectsduring each of these intervals (positives rank higher than negatives).Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The acceleration is the same for ALL SIX situations. ___

OR, The acceleration is zero for ALL SIX situations. ___

OR, We cannot determine the ranking for the acceleration for these situations. ___


Answer: A=B = C > E =F > DThe acceleration is equal to the positive or negative slope of the graphs of velocity vs time.


NT3F-RT4: VELOCITY VS. TIME GRAPHS—ACCELERATION OF OBJECTSShown below are graphs of velocity versus time for four seconds for six objects with different massesthat move along a straight, horizontal surface under the action of a force exerted by an external agent.

2 s

A

4 s0

+2 m/s

–2 m/s

2 s

B

4 s0

+2 m/s

–2 m/s

2 s

C

4 s0

+2 m/s

–2 m/s

2 s

D

4 s0

+2 m/s

–2 m/s

2 s

E

4 s0

+2 m/s

–2 m/s

2 s

F

4 s0

+2 m/s

–2 m/s

Rank these situations from greatest to least on the basis of the acceleration of these objectsduring each of these intervals (positives rank higher than negatives).Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The acceleration is the same for ALL SIX situations. ___

OR, The acceleration is zero for ALL SIX situations. ___

OR, We cannot determine the ranking for the acceleration for these situations. ___


Answer: A=B = C > E =F > DThe acceleration is equal to the positive or negative slope of the graphs of velocity vs time. It does not

depend on the mass of the objects.


NT3G-RT1: POSITION VS. TIME GRAPH—AccelerationThe graph below shows the position versus time graph for the motion of an object moving in onedimension. Six points are marked on the parabolic curve.

A

Time (s)

Position (m)

BC

D

E

F

Rank the six points on the basis of the acceleration of the object at that instant.

Greatest 1 _______ 2 _______ 3 _______ 4 _______ 5 _______ 6 _______ Least

OR, The object’s acceleration at ALL SIX points is the same. ___

OR, The object’s acceleration at ALL SIX points is zero. ___

OR, We cannot determine the ranking for the object’s acceleration at these points from this graph.___


ANSWER: SAME. The fact that the graph is a smooth parabola shows that the object’s acceleration isconstant throughout.


NT3G-QRT1: POSITION VERSUS TIME GRAPHS—Acceleration and VelocityThe graphs below show the position versus time graphs for sailboats traveling in a long narrowchannel. The scales on both axes are the same for all the graphs. In each graph a point is marked witha dot.

Position

Time

A Position

Time

B Position

Time

C

Position

Time

EPosition

Time

D Position

Time

F

Position

Time

HPosition

Time

G Position

Time

I

1. For which of these, if any, are the accelerations zero at the indicated point? _______acceleration is zero for A

2. For which of these, if any, are the accelerations negative at the indicated point? _______accelerations are negative for C, E, F, and H

3. For which of these, if any, are the accelerations positive at the indicated point? _______accelerations are positive for B, D, G, and I

4. For which of these, if any, are the velocities zero at the indicated point? _______E

5. For which of these, if any, are the velocities negative at the indicated point? _______D, F, G, I

6. For which of these, if any, are the velocities positive at the indicated point? _______A, B, C, H

7. For which of these, if any, are the positions zero at the indicated point? _______C

8. For which of these, if any, are the positions negative at the indicated point? _______A, B, D, F, H

9. For which of these, if any, are the positions positive at the indicated point? _______E, G, I

nT3 One-D Motion 8-21-#27AA - School District of Clayton Field Test version © nTIPERs nT3 1-D...

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