The acceleration of a particle depends on displacement covered in a time as `a = s + 5`. It is given that initially `s = 0` and `v = 5 m//s`, then which of the following is possibly correct ?

Options

A. `v = s + 5`
B. `v = sqrt(s + 5)`
C. `v = "log"_(e) ((s + 5)/(5))^(2)`
D. `v = "log"_(e) ((s + 5)/(s))`

Answer

A

Explanation

`a = s + 5`
`v (dv)/(ds) = + 5`
`underset(s)overset(v)(int) vdv = underset(0)overset(s)(int) v ds + underset(s)overset(s)(int) 5 ds`
`[(v)/(2)]_(s)^(v) = (s^(2))/(2) + 5s`
`(v^(2) - 2s)/(2) = (s^(2) + 10s)/(2)`
`v^(2) = s^(2) + 10s + 2s`
`v^(2) = (s + 5)^(2)`
`v = +- (s + 5)`
`v = s + 5`