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) = bt

2 − ct

3

, where b = 2.40m/s

2

and c = 0.120 m/s

3

.

(a) Calculate the average velocity of the car for the time interval t = 0 to t = 10 seconds.

(b) Calculate the instantaneous velocity of the car at t = 0,t = 5s, and t = 10s.

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

Answer 1

$$x(t)=bt^2-ct^3\\ =2.40t^2-0.120t^3$$

(a)

$$v_{ave}=\frac{\Delta v}{\Delta t}=\frac{2.40*10^2-0.120*10^3}{10}=12\:\rm m/s$$

(b)

$$v(t)=x'(t)=4.80t-0.360t^2$$

$$v(0)=4.80*0-0.360*0^2=0\:\rm m/s$$

$$v(5)=4.80*5-0.360*5^2=15\:\rm m/s$$

$$v(10)=4.80*10-0.360*10^2=12\:\rm m/s$$

(c)

$$v=4.80*t-0.360*t^2=0$$

$$t=\frac{4.80}{0.360}=13.3\:\rm s$$