Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1: 8: 1$ and the maximum speed attained be $60 \mathrm{~km} / \mathrm{h}$, then what is the average…

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Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1: 8: 1$ and the maximum speed attained be $60 \mathrm{~km} / \mathrm{h}$, then what is the average speed over the whole journey?

Aicharya · Accepted Answer

Given $u=0$. Let during three phases time taken are $t, 8 t$. and $t$, respectively. $v_{\max }=a t=60 \mathrm{~km} / \mathrm{h}$ $\begin{aligned} v_{\mathrm{av}} &=\frac{\frac{1}{2} a t^{2}+v_{\max } 8 t+\frac{1}{2} a t^{2}}{t+8 t+t}=\frac{a t^{2}+8 v_{\max } t}{10 t}=\frac{a t+8 v_{\max }}{10} \ &=\frac{60+8 \times 60}{10}=54 \mathrm{~km} / \mathrm{h} \end{aligned}$ /

Between two stations a train starting from rest first accelerates uniformly, then moves with constant…

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