Question

A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.

Answer 1

Step 1: Given data

1. The initial velocity(u) of the train is zero because the train starts from the rest.
2. The final velocity(v) of the train is $40\mathrm{km}/\mathrm{h}=\frac{5}{18}\times 40=\frac{200}{18}\mathrm{m}/\mathrm{s}$.
3. The time taken to attain the velocity is $10\mathrm{minutes}=10\times 60=600\sec$.

Step 2: Finding the acceleration

Using 1st equation of motion,

$\mathrm{v}=\mathrm{u}+\mathrm{at}$

Where, “v” and “u” are the final and initial velocities, “a” is a constant acceleration, and "t" is time.

$$\begin{gathered} \mathrm{Given},\mathrm{u}=0. \\ \Rightarrow v=at \\ \Rightarrow \frac{200}{18}=a\times 600 \\ \Rightarrow a=\frac{1}{54}=0.0185m/s^2 \end{gathered}$$

Hence, the acceleration of the train will be 0.0185 m/s^2. .