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Chapter 3Describing Motion
Scalar A quantity that has only magnitude.
Time (t) Mass (m) Distance (d) Temperature (T) Speed (s)
Chapter 3 Describing Motion
Vector A quantity with magnitude and direction
Velocity (V) Displacement (D) Force (N) Weight (N)
Chapter 3Describing Motion
Displacement The distance and direction between two positions.
Average Velocity The ratio of the change in position to the time interval during which the change occurred.
Average Speed The ratio of the total distance traveled to the total time
interval.
Chapter 3Describing Motion Average Velocity
Displacement
v dt
d1 do
t1 to
d v t
d
do d1
d
do d1
v
m/s3.80s6s0m50mV
Chapter 3Describing Motion Instantaneous velocity The speed
and direction of an object at a particular time.
The symbol for instantaneous velocity is represented by the symbol v.
Relative velocity The velocity of an object in relationship to another object
Chapter 3Describing Motion Average Acceleration
a vt
v1 vo
t1 to
Solution:The two bicycleswill meet in onehour and if the bee travels at 30 km/hr. The beewill travel 30 km.
When the Smiths went on their vacation they traveled at 40 km/hr. They returned home at a rate of 60 km/hr.
QUESTION:What was their average rate of speed?
40 km/hr>
60 km/hr
Chapter 3 Describing Motion
vdt
d1t1
d2t2
butd1 d2 d and t1 d
40, t2 d
60
v2d
d40 d
60multiplytop andbottom by120
v 2dd
40 d
60120 240d
3d 2d 240d5d 48mph
Solution
a vf vi
t f t ibut if ti = 0, then vf = vi + at
d v t but v vi v f
2so d
v i v f
2
t
d vi v f
2
t
Substitute for vf d vi vi at
2
t
d v it 12
at2
Chapter 3 Describing Motion
vf = vi + at d vi v f
2
t
Solve both equations for t
v f v i
a
2dvi vf
t 2d
vi v f
Set equal to each other
t vf vi
aMultiply across
(vf - vi)(vi + vf) = 2ad
Simplify
vf 2 = vi
2 + 2ad
Chapter 3 Describing Motion
vf = vi + at
d vi v f
2
t
vf 2 = vi
2 + 2ad
Chapter 3 Describing Motion
d v it 12
at2
ag = -9.8 m/s2
ag = -32 ft/s2
tvva if
d v t
Ima Hurryin approaches a stoplight in her car which is moving with a velocity of +30.0 m/s. The light turns yellow, Ima applies the brakesand skids to a stop. If Ima's acceleration is –8.00 m/s2, determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a positive (+) and a negative (–) sign, respectively.)
Chapter 3Describing Motion
Diagram:
Given:vi = +30.0 m/svf = 0 m/sa = –8.00 m/s2
Find:d = ??
Chapter 3Describing Motion
•(0 m/s)2 = (30.0 m/s)2 + 2*(-8.00 m/s2)*d •0 m2/s2 = 900 m2/s2 + (-16.0 m/s2)*d•(16.0 m/s2)*d = 900 m2/s2 - 0 m2/s2
•(16.0 m/s2)*d = 900 m2/s2
•d = (900 m2/s2)/ (16.0 m/s2)•d = 56.3 m
advv 22i
2f
Chapter 3Describing Motion
Ben Rushin is waiting at a stoplight in his car,When the light turns green, Ben accelerates from rest at a rate of a 6.00 m/s2 for an interval of 4.10 seconds. Determine the displacement of Ben's car during this timeperiod. Given: Find:
vi = 0 m/s d =? t = 4.10 sa = 6.00 m/s2
Chapter 3Describing Motion
•d = (0 m/s)*(4.1 s) + 0.5*(6.00 m/s2)*(4.10 s)2 •d = (0 m) + 0.5*(6.00 m/s2)*(16.81 s2)•d = 0 m + 50.43 m•d = 50.4 m
Chapter 3Describing Motion
2
21 attvd i
Luke Autbeloe drops a pile of roof shingles from thetop of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.
Given: Find:vi = 0.0 m/s t = ?? d = –8.52 ma = –9.8 m/s2
Chapter 3Describing Motion
•-8.52 m = (0 m/s)*(t) + 0.5*(-9.8 m/s2)*(t)2 •-8.52 m = (0 m) *(t) + (-4.9 m/s2)*(t)2
•-8.52 m = (-4.9 m/s2)*(t)2
•(-8.52 m)/(-4.9 m/s2) = t2
•1.739 s2 = t2
•t = 1.32 s
Chapter 3Describing Motion
2
21 attvd i
Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.
Given: Find:
vi = 26.2 m/s d = ?? vf = 0 m/sa = –9.8 m/s2
Chapter 3Describing Motion
•(0 m/s)2 = (26.2 m/s)2 + 2*(-9.8m/s2)*d •0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2)*d•(-19.6 m/s2)*d = 0 m2/s2 -686.44 m2/s2
•(-19.6 m/s2)*d = -686.44 m2/s2
•d = (-686.44 m2/s2)/ (-19.6 m/s2)•d = 35.0 m
Chapter 3Describing Motion
advv 22i
2f
An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until it finally lifts off the ground. Determine the distance traveled before take-off.•Given:•a = 3.20 m/s2
•t = 32.8 s•vi = 0 m/s
•Find:•d = ??
Chapter 3Describing Motion
•d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2
•d = 1720 m
2
21 attvd i
Upton Chuck is riding the Giant Drop at Great America. If Upton free-falls for 2.6 seconds, what will be his final velocity and how far will he fall?
•Find:•d = ?? •vf = ??•d = vi*t + 0.5*a*t2 •d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s2)*(2.6 s)2
•d = 33 m
•vf = vi + a*t•vf = 0 + (-9.8 m/s2)*(2.6 s)
•vf = -25.5 m/s (the negative sign indicates direction)
•Given:•a = –9.8 m/s2
•t = 2.6 s•vi = 0 m/s
Chapter 3Describing Motion
A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike.
•vf2 = vi
2 + 2*a*d•(7.10 m/s)2 = (0 m/s)2 + 2*(a)*(35.4 m)•50.4 m2/s2 = (0 m/s)2 + (70.8 m)*a•(50.4 m2/s2)/(70.8 m) = a•a = 0.712 m/s2
Chapter 3Describing Motion
A car is traveling at 65 km/hr. The brakesare applied and the car stops in 3 seconds.a. What is the car’s acceleration?b. How far does it travel?
vi = 65 km/hrt = 3 svf = 0
vi = 65 km/hr = 18m/s
Chapter 3Describing Motion
Chapter 3Describing Motion
A car is traveling at 65 km/hr. The brakesare applied and the car stops in 3 seconds.a. What is the car’s acceleration?b. How far does it travel?
vi = 18 m/st = 3 svf = 0
ssm
tvv
a if
3/180
2/6 sma
Chapter 3Describing Motion
A car is traveling at 65 km/hr. The brakesare applied and the car stops in 3 seconds.a. What is the car’s acceleration?b. How far does it travel?
2
21 attvd i
22 )3)(/6(21)3)(/18( ssmssmd =27 m
Chapter 3Describing Motion
An airplane must reach a speed of 55 m/sbefore take off. It can accelerate at 12 m/s2.a. How long does the runway have to be?b. How long will this take?
vi = 0a = 12 m/s2
vf = 55 m/s
advv if 222
mavv
d if 1262
22
Chapter 3Describing Motion
An airplane much reach a speed of 55 m/sbefore take off. It can accelerate at 12 m/s2.a. How long does the runway have to be?b. How long will this take?
vi = 0a = 12 m/s2
vf = 55 m/savv if t
ssm
smsm 58.4/12
/0/552
t
Chapter 3Describing Motion
Joe is driving a car at 20 m/s and notices a cow in front of him at a distance of 80 m away. He brakes at a rate of 3 m/s2. What happens to the cow?
vi = 20 m/sa = -3 m/s2
vf = 0
Chapter 3Describing Motion
avv
d if
2
22
)/3(2)/20(0
2
2
smsmd
md 7.66
The cowsurvives!!!!
ag = -9.8 m/s2
For all free falling bodies on earth, theyacceleratedownward at 9.8 m/s2.
Chapter 3Describing Motion
A ball is thrown upward at 49 m/s.a. How long is it in the
air?b. How high does it
go?c. How fast is it going
when it lands?
Chapter 3Describing Motion
How long is it in the air? vi = 49 m/sa = -9.8 m/s2
vf = 0avv if t 2/8.9
/490smsm
t
sec5t Total time in air is 10 sec
Chapter 3Describing Motion
How high does it go?
vi = 49 m/sa = -9.8 m/s2
t = 5 sec
2
21 attvd i
22 )5)(/8.9(21)5)(/49( ssmssmd
md 5.122
Chapter 3Describing Motion
How fast is it going when it lands?
vi = 49 m/sa = -9.8 m/s2
t = 10 secatvv if
)10)(/8.9(/49 2 ssmsmv f
smv f /49
Chapter 3Describing Motion
Chapter 3Describing Motion
Free Fall
A skier travels from A to B to C to D.What is her average velocity and speed?
Chapter 3Describing Motion
Josh travels from A to B to C to D.What is his average velocity and speed?
Chapter 3Describing Motion
min3m140
v =46.7 m/min
min3m420
s =140 m/min
When a traffic light turns green, a waiting car starts off with a constant acceleration of 6 m/s2. At the instant the car begins to accelerate, a truck with constant velocity of 21 m/s passes in the next lane.
a. How far will the car travel before it overtakes the truck? b. How fast will the car be traveling when it overtakes the truck? c. Construct a distance vs time graph for the car and the truck on the same graph.
Chapter 3 Describing Motion