Question

a driver of the car travelling with a uniform velocity of 2m/s notices a railway level crossing at distance of 500 m from him a train approaching the level crossing with a uniform velocity of 90 km/h is at distance of 1 km from the level crossing calculate at what rate the driver of the car has to increase velocity of the car so that he reaches the gates of level crossing exactly when the train enters the level crossing also find the final velocity of car when it reaches the level crossing.

Answer 1

"The car has to accelerate at the rate of $0.525 m s^{-2}$ in order to reach the crossing at the same time as the train.

Solution:

We know that,

Velocity $= \frac { Displacement }{Time}$

Velocity of car = 2 m/s

Velocity of train $=90 \mathrm{kmhr}^{-1}=\frac{90 \times 1000}{60 \times 60}=25 \mathrm{ms}^{-1}$

Time taken by the train to reach the crossing $=\frac{1000}{25}=40 s$

Thus, the car has to cross 500m in 40s to reach the crossing.

We know that distance travelled by an object is given by,

$s=u t+\frac{a t^{2}}{2}$

Here, s = 500, t = 40, u = 2m/s

$\Rightarrow 500=(2 \times 40)+\left(a \times \frac{40^{2}}{2}\right)$

500=80+800 a

$a=\frac{500-80}{800}$

$a=0.525 m s^{-2}$"