Question

A moving train is brought to rest within 10 seconds by applying brakes. What is the initial velocity, if the retardation due to brakes is 2.5 ms^-2?

Answer 1

Step 1:Given data:

1. Retardation due to brakes is 2.5 m/s².
2. The train is brought to rest means that the final speed of the train will be zero.

Step 2: Finding the initial velocity (u):

Now we know that;

1. Acceleration (retardation in this case) is defined as the rate of change in velocity.
2. From the first equation of motion we have $v=u+at$.

Where,

1. v is the final velocity of the train.
2. u is the initial velocity of the train.
3. a is the constant acceleration (retardation) of the train.
4. t is the time.

We have,

Final velocity (v) = 0, a = -2.5 m/s² (because of retardation), t = 10 s.

Therefore,

$$\begin{gathered} v=u+at \\ 0=u+(-2.5)\times 10 \\ 0=u-25 \\ u=25m/s. \end{gathered}$$

Hence, the initial velocity is equal to 25 m/s.