Find the initial velocity of a train, which is stopped in 20 s by applying brakes. The retardation due to brakes is $1.5m/s^2$.

Step 1: Given data

Acceleration of the train, $a=-1.5m/s^2.$

Acceleration is negative as brakes are applied, Therefore acceleration is acting in opposite direction of motion.

Required time, t = 20 s.

Final velocity, v = 0 m/s.

Step 2: Finding the initial velocity of the train

Let u is the initial velocity of the train.

Now, from the Newton's first equation of motion;

$v=u+at.$………(1)

Where v and u are the final and initial velocities respectively.

And t is the time.

From equation (1)

$$\begin{gathered} 0=u+\left\{(-1.5)\times 20\right\}. \\ 0=u-30. \\ u=30m/s. \end{gathered}$$

Hence, the initial velocity of the train is $30m/s.$