Question

A bus starts from rest and moves with constant acceleration $8{ms}^{-2}$. At. the same time, a car travelling with a constant velocity 16 m/s overtakes and passes the bus. After how much time and at what distance, the bus overtakes the car?

• A. $t=4s,d=64m$
• B. $t=5s,d=72m$
• C. $t=8s,d=58m$
• D. None of the above

Answer 1

The correct option is A $t=4s,d=64m$

The position of bus after time $t$ is given as $x_b=\frac{1}{2}a{t}^2$

The position of car after time $t$ is given as $x_c=ut$

Hence when the bus passes the car,

$x_b=x_c$

$⟹\frac{1}{2}a{t}^2=ut$

$⟹t=\frac{2u}{a}$ $=\frac{2\times 16m/s}{8m/s^2}$ $=4s$

Hence the distance at the crossing=$ut=16m/s\times 4s=64m$