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 $2:1:2$ and the greatest speed is $10\text{km/hr}$, find the average speed over the whole journey.

• A. $6\text{km/hr}$
• B. $9\text{km/hr}$
• C. $4.5\text{km/hr}$
• D. $3\text{km/hr}$

Answer 1

The correct option is A $6\text{km/hr}$

Let, the time taken to travel second part of the journey be $t$, where the train accelerates with constant acceleration.

Since, the ratio of the times are $2:1:2$ so, the time taken to travel the part of the journey is $2t$ and time taken to the third part of the journey is $2t$.

Below, given $v-t$ graph shows the motion.


Average speed of the journey,

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

$=\frac{\frac{1}{2}\times 10\times 2t+10\times t+\frac{1}{2}\times 10\times 2t}{5t}$

$=\frac{30t}{5t}=6\text{km/h}$

Hence, $\left(A\right)$ is the correct answer.