MP Board · Class 9 · Science · MotionA train starting from rest attains a velocity of $72\text{ km/h}$ in $5\text{ minutes}$. Assuming that the acceleration is uniform, find the acceleration of the train.

Given:\nInitial velocity ($u$) = $0\text{ m/s}$ (starts from rest)\nFinal velocity ($v$) = $72\text{ km/h} = 72 \times \frac{5}{18} = 20\text{ m/s}$\nTime taken ($t$) = $5\text{ minutes} = 5 \times 60 = 300\text{ seconds}$ \nFormula:\nAcceleration ($a$) is given by the equation of motion: $$a = \frac{v - u}{t}$$ \nCalculation: $$a = \frac{20 - 0}{300} = \frac{20}{300} = \frac{1}{15}\text{ m/s}^2 \approx 0.067\text{ m/s}^2$$ \nThus, the uniform acceleration of the train is $\frac{1}{15}\text{ m/s}^2$ or $0.067\text{ m/s}^2$. Acceleration is defined as the rate of change of velocity per unit time. Here, the train steadily increases its speed from zero to $20\text{ m/s}$ over $300\text{ seconds}$, yielding a constant rate of acceleration.