Problem: A moving train is brought to rest within 20 seconds by applying brake. Find the initial velocity if the retardation due to break is 2ms?

Solution:
To solve the problem, we can use the following formula:

v = u - at

Where:
v = final velocity (0 m/s)
u = initial velocity (unknown)
a = acceleration (retardation due to break = -2 m/s²)
t = time (20 seconds)

Substituting the given values in the formula, we get:

0 = u - (-2) x 20
0 = u + 40
u = -40 m/s

However, the negative sign indicates that the train was moving in the opposite direction to the applied brake force. Therefore, we need to take the absolute value of the initial velocity:

|u| = 40 m/s

Therefore, the initial velocity of the train was 40 m/s.

Explanation:
When the brake is applied, it generates a force that acts in the opposite direction to the motion of the train. This force causes a negative acceleration (retardation) that reduces the velocity of the train. The rate of retardation is given by the formula:

a = (v - u) / t

Where:
v = final velocity (0 m/s)
u = initial velocity (unknown)
t = time (20 seconds)

Substituting the given values, we get:

-2 = (0 - u) / 20

Solving for u, we get:

u = -2 x 20
u = -40 m/s

This means that the velocity of the train was initially 40 m/s in the opposite direction to the applied force. To find the absolute value of the initial velocity, we take the absolute value of -40, which is 40 m/s. Therefore, the initial velocity of the train was 40 m/s.

In this question :v=0(comes at rest) u=?(to find) t=20sec.(given) a=2m/sby first equation of motion (v=u+at)0=u+2*200=u+400-40=u-40=u