Question

Brakes are applied to a train travelling at75km/hr.after passing over 200m,its velocity is reduced to 36km/hr.at the same rate of retardation,how much further it will go before coming at rest.

Answer 1

Answer on Question #46358, Physics, Mechanics | Kinematics | Dynamics

Brakes are applied to a train travelling at 75km/hr.after passing over 200m, its velocity is reduced to 36km/hr.at the same rate of retardation,how much further it will go before coming at rest.

Solution

Velocities in m/s are: $v_{0}=75km/hr\approx 20.8\,m/s$, $v_{1}=36km/hr=10\,m/s$. Lets find deceleration. We need two equations: for distance and for velocity. Here they are:

$s=v_{0}t-at^{2}/2$

$v=v_{0}-at$

From those we can first time of first part of way:

$s_{1}=v_{0}t_{1}-(v_{1}-v_{0})t_{1}/2$

$t_{1}=\frac{s_{1}}{v_{0}/2-v/2}=\frac{200}{20.8/2-10/2}\approx 37\,s$

Hence deceleration is

$a=\frac{v-v_{0}}{t}=\frac{20.8-10}{37}\approx 0.29\,m/s^{2}$

Hence, it will take time:

$t_{2}=\frac{10}{0.29}\approx 34.5\,s$

to decelerate to