Question

A car and a truck move in the same straight line at the same instant of time from the same place. The car moves with a constant velocity of $40m/s$ and the truck starts with a constant acceleration of $4m/s^2$. Find the time $t$ that elapses before the truck catches up with the car.

• A. $10s$
• B. $20s$
• C. $30s$
• D. $40s$

Answer 1

The correct option is B $20s$

Initial velocity of car, $u_c=40m/s$
Initial velocity of truck, $u_T=0$
Acceleration of the truck = $a_T$
Acceleration of the car, $a_c=0$.
Let the displacement of car w.r.t truck be $S_{cT}$
When the truck meets the car, $S_{cT}=0$
Using second equation of motion,
$S_{cT}=u_{cT}t+\frac{1}{2}{a}_{cT}{t}^2$
$0=(u_c-u_T)t+\frac{1}{2}(a_c-a_T)t^2$
$0=(40-0)t+\frac{1}{2}(0-4)t^2$
$2t^2=40t⟹2t=40$
$\therefore t=20s$