A train is traveling at a speed of . Brakes are applied so as to produce a uniform acceleration of . Find how far the train will go before it is brought to rest.

Concept: Equation of motion: These are the mathematical equations used to find the final velocity, displacements, time, and so on of a moving object without taking into account the force acting on it.

These equations are only valid when the body's acceleration is constant and it moves in a straight line.

There are three types of motion equations:

Here, final velocity, initial velocity, distance traveled by the body under motion, a = acceleration of body under motion, and time taken by the body under motion.

Initial velocity

Acceleration

Since the train comes to rest,

Final velocity

We need to find the distance

and we know v, u and a

So, we use the third equation of motion

From the third equation of motion,

Therefore, the train will cover a distance of before coming to rest