An object moves in such a way that when it has moved a distance s its velocity is v=sqrts, how do you find its acceleration?

1 Answer
Dec 15, 2016

acceleration = 1/2

Explanation:

The velocity, v, is defined as v=(ds)/dt, and the acceleration, a is given by a=(dv)/dt

We are told that v=sqrt(s)

:. (dv)/(ds) = 1/2s^(-1/2)
" " = 1/(2sqrt(s))

So using the chain rule we can write:

a = (dv)/dt
\ \ = (dv)/(ds) * (ds)/dt
\ \ = (1/(2sqrt(s))) * v
\ \ = (1/(2sqrt(s))) * sqrt(s)
\ \ = 1/2