Question

The velocity 'u' of a body moving along a straight line with constant retardation 'a' reduced by 75% in time t. What is the time taken in doing so

Answer 1

Given: The velocity 'u' of a body moving along a straight line with constant retardation 'a' reduced by 75% in time t.

To find: Time taken in the process

Solution: Let the final velocity be v.

Now, u is reduced by 75%. Therefore, final velocity (v)

= u - 75% of u

= u - (75/100) × u

= u - 0.75 u

= 0.25 u

Therefore, v = 0.25 u

Here, since acceleration is negative, acceleration is denoted as -a.

Now, using kinematics equation:

v = u + at

=> 0.25 u = u +(-a) t

=> 0.25u-u = -at

=> -0.75u = -at

=> t = 0.75u/a

Therefore, the time taken in doing so is equal to 0.75u/a.