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 = 2.60m/s2 and c = 0.130 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?

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Explanation / Answer

a)

t1 = 0

x1 = 0

t2 = 10

x2 = (2.6*10^2) - (0.13*10^3) = 130 m

average velocity Vav = (x2-x1)/(t2-t1) = (130-0)/10 = 13 m/s

(b)

v(t) = dx/dt = 2bt - 3ct^2

at t = 0

v = 0

(c)

at time t = 5 s

v = (2*2.6*5)-(3*0.13*5^2) = 16.25 m/s

(d)

v10 = (2*2.6*10)-(3*0.13*10^2) = 13 m/s

(e)

speed v = 0

2bt - 3ct^2 = 0

2b = 3ct

t = 2b/3c

t = (2*2.6)/(3*0.13) = 13.33 m/s

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