Question

5.) A car traveling at 15 m/s passes a van that is starting from rest with an acceleration of 3 m/s². (a) How long will it take the van to catch up with the car? (b) How far has the car traveled when the van catches up with it?

Answer 1

Let after time $t \space sec$ ,van catches up the car.

(a) So,distance traveled by car in $t$ seconds:

$u_{car}t=u_{van}t+\frac{1}{2} at^2 ;u_{van}=0$

$15 t=\frac{1}{2}\times a \times t^2$

$a=3 m/sec ^2$

Solving this equation :

$15 t=\frac{1}{2}\times 3 t^2$

$t=10 \space sec$

(b) Distance traveled by car in $10 \space sec =$ $\space u_{car}t=15 \times 10=150 m$