A man is $48 m$ behind a bus which is at rest. The bus starts accelerating at the rate of $1 m / s^{2}$ , at the same time the man starts running with uniform velocity of $10 m / s$ . What is the minimum time in which the man catches the bus?

Open in App

Solution

Given,

Acceleration of bus, $a = 1 m s^{- 2}$

Assume man catches the train in time $t$ .

Displacement by man in time $t$ $s_{1} = v t = 10 t$

Displacement by bus in time t, $s_{2} = u t + \frac{1}{2} a t^{2} = \frac{t^{2}}{2}$

Separation between man and bus is $48 m$

$s_{1} = s_{2} + 48$

$10 t = \frac{t^{2}}{2} + 48$

$t^{2} - 20 t + 96 = 0$

$t = \frac{20 \pm \sqrt{20^{2} - 4 \times 96}}{2}$

$t = 8 a n d 12$

In first attempt he caches the bus

Hence, minimum time he catches the bus is $8 sec$

Suggest Corrections

Similar questions

Q. A bus starts from rest with an acceleration of

1.0 m / s^{2}

. A man who is

48 m

behind the bus, starts with a uniform velocity of

10 m / s

. Find the minimum time after which the man will catch the bus.

Q. A bus at rest starts accelerating at 1 m/s. A man 50 m behind it runs to catch the bus. At what minimum speed should he run to catch the bus

A bus starts to move with acceleration 1m/s^2. A man who is 48 m behind the bus runs to catch it with a constant velocity of 10 m/sec. In how much time he will catch the bus?

Q. A man is 45 m behind the bus when the bus start accelerating from rest with acceleration

2.5

. With what minimum velocity should the man start running to catch the bus

Q. A man is

d

distance behind a bus. The bus starts moving away from the man with an acceleration

a

. At the same time man starts running towards the bus with a constant velocity

v

Join BYJU'S Learning Program

A man is 48m behind a bus which is at rest. The bus starts accelerating at the rate of 1m/s2, at the same time the man starts running with uniform velocity of 10m/s. What is the minimum time in which the man catches the bus?

A man is $48 m$ behind a bus which is at rest. The bus starts accelerating at the rate of $1 m / s^{2}$ , at the same time the man starts running with uniform velocity of $10 m / s$ . What is the minimum time in which the man catches the bus?