Question

s. A car is stopped at a traffic light. It then travels along a straight road such that its distance trom the light is given by X(t)-3.5t-o.st. (a) What is the instantaneous velocity of the car att 4.0s. (b) How long after starting from rest is the car again at rest?

Answer 1

a) The velocity is

$v=\frac{dx}{dt}=\frac{d}{dt}(3.5 t^2-0.5t^3)=7.0\, t-1.5\, t^2$

At t = 4.0 s

the instantaneous velocity is

$v=7.0\times 4 -1.5\times 4^2=4\,m/s$

b) when the car comes to rest

$x=0$

this gives

OR

Hence

$t=7\,s$

It will come to rest after 7 seconds