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Relative Acceleration

A car and a t...

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 $40 m / s$ and the truck starts with a constant acceleration of $4 m / s^{2}$ . Find the time $t$ that elapses before the truck catches up with the car.

A

10 s

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B

20 s

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C

30 s

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D

40 s

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Solution

The correct option is B $20 s$
Initial velocity of car, $u_{c} = 40 m / s$
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 $S_{c T}$
When the truck meets the car, $S_{c T} = 0$
Using second equation of motion,
$S_{c T} = u_{c T} t + \frac{1}{2} a_{c T} t^{2}$
$0 = (u_{c} - u_{T}) t + \frac{1}{2} (a_{c} - a_{T}) t^{2}$
$0 = (40 - 0) t + \frac{1}{2} (0 - 4) t^{2}$
$2 t^{2} = 40 t ⟹ 2 t = 40$
$∴ t = 20 s$

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