Question

A particle moves along a straight line with acceleration a = (2 - 3s), where the unit for a is m/s^2 and s is m. Write down the relationship between the velocity with the displacement of the particle if given s = 4 m ,the velocity of the particle v = 2m/s?

Answer 1

a=2-3s

$a=v\frac{dv}{ds}$

$v dv=(2-3s) ds$

Integrating both the sides

$\int\limits^2_0{v} \, dv=\int\limits^4_0 {(2-3s)} \, ds$

$\frac{v^2}{2} =2s-\frac{3s^2}{2}$