Graphs of MotionDistance/Time or Position/Time Graph:• Flat line = stopped• Sloping up = constant speed away• Sloping down = constant speed back towards start• Curved line = changing speed = accelerating

How Can You Create the Following Position Graphs?

X(m)

t (sec)

X(m)

t (sec)

X(m)

t (sec)

X(m)

t (sec)

A. Speed Up B. Turn Around C. Slow Down D. Stand Still

Graph 1. Graph 2.

Graph 4.Graph 3.

Velocity/Time Graph:• Flat line = constant speed• Sloping up = acceleration away• Sloping down = acceleration towards/slowing down• Zero = stopped

How Can You Create the Following Velocity Graphs?

A. Speed Up, then Slow Down B. Turn Around C. Walk AwayD. Stand Still E. Walk Toward

V(m/s)

t (sec)0

V(m/s)

t (sec)0

V(m/s)

t (sec)0

V(m/s)

t (sec)0

Graph 1.

Graph 3.

Graph 2.

Graph 4.

Which Object is Moving Faster (Greatest Speed)?

X(m)

t (sec)

X(m)

t (sec)

X(m)

t (sec)

X(m)

t (sec)

A. Line A B. Line B C. Tie D. Can’t Tell

A

B

B

BB

A

A

A

Graph 1.

Graph 3.

Graph 2.

Graph 4.

Which Object is Moving Faster (Greatest Speed)?A. Line A B. Line B C. Tie D. Can’t Tell

A

B V(m/s)

t (sec)0

Which Object is Ahead?A. Line A B. Line B C. Tie D. Can’t Tell

Which Object is Moving Faster (Greatest Speed)?A. Line A B. Line B C. Tie D. First B, then

AB. E. First A, then B

Which Object is Ahead?A. Line A B. Line B C. Neither D. Can’t

TellWhat Does the Intersection Represent?

A. Same Position B. Same Velocity

C. They Crash Into Each Other D. They Turn Around

V(m/s)

t (sec)0

B

A

Create a Velocity Graph from a Position Graph

Create a Velocity Graph from a Position Graph

Velocity is the Slope of the Position Graph

Create a Velocity Graph from a Position Graph

(3.0, 3.5)

(0.5, 1.0)

∆x

∆t

Slope = ∆x = 3.5 - 1.0 = +1 m/s∆t 3.0 - 0.5

Create a Velocity Graph from a Position Graph

Slope = 0Velocity = 0

Create Position Graph from a Velocity GraphDoes the Velocity Graph tell you Where to Start?

Line Stays at 1 m while Velocity is ZeroHow Far Do You Go from 3 to 6 seconds?

You end up at 2.5 meter Position at 6 secondsHow Far Do You Go from 6 to 9 seconds?

You End Up Back Where You StartedWhat Does the Graph Do Next?

What is Average Speed While Moving?What is the Average Velocity While Moving?

What is Average Speed While Moving?What is the Average Velocity While Moving?

What is Average Speed While Moving?What is the Average Velocity While Moving?

Area “Under” a Velocity Graph is Displacement

0.5 m/s 3 s = 1.5 m

-0.5 m/s 3 s = -1.5 m

+1.5 m -1.5 m

Area “Under” a Velocity Graph is Displacement,even when Velocity Line has a Slope

Area “Under” a Velocity Graph is Displacement,even when Velocity Line has a Slope

Area = 1/2 4s .5 m/s = 1m

Area = 1/2 2s .5 m/s = 0.5 m

Area = 4s .5 m/s = 2 m

Or, Displacement is the Average Velocity times the Time

E&P #17

1. When, if ever, is the animal to the left of the origin on the axis? (A) never (B) between t = 0 and t = 2 (C) none of these (D) between t = 2 and t = 4 (E) between t = 4 and t = 7

2. When, if ever, is its velocity negative? (A) never (B) between t = 3 and t = 7 (C) none of these (D) between t = 0 and t = 3 (E) between t = 2 and t = 4

3. When, if ever, is its velocity positive?

(A) always (B) between t = 3 and t = 7 (C) none of these (D) between t = 0 and t = 3 (E) never

4. When, if ever, is its velocity zero? (A) around t = 1 (B) at t = 3 (C) between t = 2.5 and t = 4.5 (D) never (E) at t = 0

+

0

-

E&P #19

1. What is the total distance covered between 0 and 16 seconds by the runner whose velocity is shown above?(A) 128 m(B) 80 m(C) 100 m(D) Can’t tell(E) None of the above

Which Graph Shows the Velocity of a Ball Thrown Straight Up, After it Leaves Your Hand?

V(m/s)

t (sec)0

V(m/s)

t (sec)0

V(m/s)

t (sec)0

V(m/s)

t (sec)0

A

C

B

D

V(m/s)

t (sec)0

E