A car is stopped at a traffic light. It then travels along a straight road so th

Question

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given byx(t)=bt2ct3, where b = 2.40 m/s2 and c = 0.110 m/s3 .

Part A

Calculate the average velocity of the car for the time interval t= 0 to t= 10.0 s.

Part B

Calculate the instantaneous velocity of the car at t=0.

Part C

Calculate the instantaneous velocity of the car at t=5.00 s.

Part D

Calculate the instantaneous velocity of the car at t=10.0 s.

Part E

How long after starting from rest is the car again at rest?

Explanation / Answer

a) average velocity = total distance / total time
total distance = 2.4*100 - .11 * 10^3 = 240 - 110 = 130
average velocity = 13 m/s

b) velocity at any instant = dx/dt = 2bt - 3ct^2
at 0 seconds velocity = 0

c)at 5 seconds velocuty = 2*2.4*5 - 3*.11*25 = 15.75 m/sec
d)at 10 seconds velocity = 2*2.4* 10 - 3* .11* 100 = -15 m/sec

e) velocity is zero when 4.8 t - .33 t^2 = 0
t(4.8-.33t) = 0
eother t = 0 which is the start or 4.8-.33t = 0 or t = 14.54 seconds

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