Question

Between two stations a train accelerates uniformly at first, then moves with constant speed and finally retards uniformly. If the ratios of time taken are $1:8:1$ and the greatest speed is $60\text{km/hr}$, find the average speed over the whole journey.

• A. $25\text{kmph}$
• B. $50\text{kmph}$
• C. $54\text{kmph}$
• D. $72\text{kmph}$

Answer 1

The correct option is C $54\text{kmph}$

Below given $v-t$ graph shows the motion given in question


Given:
Maximum speed, $v_m=60\text{km/hr}$


Average speed can be dined as

$v_{avg}=\frac{\text{Area under}v-t\text{curve}}{\text{total time taken}}$

$\Rightarrow v_{avg}=\frac{(2\times \frac{1}{2}\times 60\times t)+(60\times 8t)}{10t}$

$\Rightarrow v_{avg}=54\text{km/hr}$

Hence, option $\left(c\right)$ is correct.