Answer to Question #120170 in Mechanics | Relativity for pro

Question

A train is travelling at a speed of 90 km h −1 . Brakes are applied so as to produce a
uniform acceleration of −0.5 m s −2 . Find how far the train will go before it is
brought to rest.

Answer 1

The initial speed of train is $v_0 = 90km/h = 25 m/s$ and the acceleration is $-0.5m/s^2$. According to the kinematic equation:

$$v_0 = -at$$

where $t$ is the time required to stop the train. Thus:

$$t = -\dfrac{v_0}{a} = -\dfrac{25}{-0.5} = 50s$$

The distance, traveled by train by this time is:

$$d = v_0t + \dfrac{at^2}{2} = 25\cdot 50 - \dfrac{0.5\cdot 50^2}{2} = 625 m$$

Answer. d = 625 m.