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 by x(t)=bt2ct3, where b = 2.90 m/s2 and c = 0.120 m/s3 .

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

(B) Calculate the instantaneous velocity of the car at t=0.

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

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

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

Explanation / Answer

A)

The average velocity is

V = deltax/deltaT = [X(10 ) - X(0) ]/ ( 10 -0)

V = 12 m/s

B)

Instantaneous velocity of car at t =0 = dX/dt = 2*b*t-3*c*t^2

substitute t =0 , velocity = 0 m/s

C)

instantaneous velocity of car at t =5 = dX/dt = 2*b*t-3*c*t^2

substitute t =5 , velocity = 15 m/s

D)

instantaneous velocity of car at t =10 = dX/dt = 2*b*t-3*c*t^2

substitute t =10 , velocity = -12 m/s

E)

Given the car will be at rest.

Velocity is zero when 4.8 t - .36 t^2 = 0, So,
t(4.8-.36t) = 0
eother t = 0 which is the start or 4.8-.36t = 0

t = 13.33 seconds

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