Question

a moving train is brought to rest within 20 seconds by applying brakes . find the intitial velocity , if the retardation due to brakes is 2m/s² . also calculate the distance travelled by train.

Answer 1

Given,
$$\begin{gathered} \mathrm{Final}\mathrm{velocity},\mathrm{v}=0 \\ \mathrm{Time}\mathrm{taken},\mathrm{t}=20\mathrm{seconds} \\ \mathrm{Acceleration},\mathrm{a}=-2\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{Initial}\mathrm{velocity},\mathrm{u}=? \\ \mathrm{Distance}\mathrm{travelled},\mathrm{s}=? \\ \mathrm{Using}, \\ \mathrm{v}=\mathrm{u}+\mathrm{at} \\ \mathrm{Putting}\mathrm{the}\mathrm{values}, \\ 0=\mathrm{u}+(-2)\times 20 \\ \mathrm{or}\mathrm{u}=40\mathrm{m}/\mathrm{s} \\ \mathrm{Again}\mathrm{using}{\mathrm{v}}^2={\mathrm{u}}^2+2\mathrm{as} \\ 0={40}^2+2\times (-2)\times \mathrm{s} \\ 0=1600-4\mathrm{s} \\ \mathrm{or}\mathrm{s}=\frac{1600}{4}=400\mathrm{m} \end{gathered}$$