Question

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.2 m/s^2. At the same instant a truck, traveling with a constant speed of 20 m/s overtakes and passes the car. (a) How far beyond its starting point does the car overtake the truck? (b) How fast is the car traveling when it overtakes the truck?

Answer 1

a)

From kinematic equation

x-xo=vo*t+1/2*ax*t^2

For truck,

xT=vot*

For car, xC=1/2*aC*t^2

Setting ,xT=xC

gives, t=0 and vot=1/2*aC*t

t =(2*vot)/aC

t=(2*20 m/s)/(3.20 m/s^2) =12.5 s

At this t, xT=20 m/s*12.5 s =250 m ,and xC=1/2*3.20 m/s^2*(12.5 s)^2 =250 m

The car and truck have each traveled 250 m

b)

At t=12.5 s, the car has vx=vox+ax*t =(3.20 m/s^2)*(12.5 s) =40 m/s