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) = bt2 - ct3, where b = 2.20 m/s2 and c = 0.130 m/s3.

(a) Calculate the average velocity of the car for the time interval t = 0 to t = 12.0 s.
.............m/s

(b) Calculate the instantaneous velocity of the car at the following times:
i) t = 0
.......m/s
ii) t = 6.0 s
........m/s
iii) t = 12.0 s
.........m/s

(c) How long after starting from rest is the car again at rest?
........s

Explanation / Answer

x(t) = bt^2 - ct^3

V(t) = 2bt - 3ct^2

a)

at t= 0.........xo = 0

at t= 12..........x = (2.2*12*12)-(0.13*12*12*12) = 92.16m

Vaverage = x-xo/t = 92.16/12 = 7.68 m/s

b) V(t) = 2bt - 3ct^2

i) V = 0

ii) V = ((2*2.2*6)-(3*0.13*6*6)) = 12.36 m/s

iii) V = ((2*2.2*12)-(3*0.13*12*12)) = -3.36 m/s

c) x = 0

bt^2 - ct^3 = 0

t = b/c = 2.2/0.13 = 16.92 s

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