Question

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?

Answer 1

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`