Question

 A point mass moves along a straight line with a deceleration n which is equal to K√v where K is a positive constant and v is the velocity of the particle. The velocity of the point mass at t = 0 is equal to v₀ . Find the distance it will travel before it stops and the time it will take to cover this distance.

Answer 1

In the expression for acceleration separate the variables and integrate to get the desired quantity

Let t₀ be the time which the particle takes to come to a stop.

Integrating

Let s₀ be the dist nce covered when the velocity decrease from v₀ to zero.