A body of mass `0.5` kg travels in a straight line with velocity `v = ax^(3/2) "where " a=5m^(-1/2)s^(-1)` . What is the work done by the net force during its displacement from x = 0 to x = 2 m ?

Explanation

If a body undergoes displacement dx, then work done by the force W = ma dx .
` :. W = m (dv)/(dt) .dx `
`= m (dx)/(dt) .dv `
= mv dv
` :. W = int dW = m int_(0)^(2) " v dv" =1/2 mv^(2)`
` = 1/2 m (ax^(3/2))_(0)^(2)`
` = 1/2 "ma"^(2)x^(3)`
` = 1/2 xx 1/2 xx(5)^(2) xx(2)^(3)`
= 50 J