A particle of mass 10   g   moves in a straight line with retardation 2 x , where x is the displacement in SI units. Its loss of kinetic energy for above displacement is 10 x - n J . The value of n will be _ _ _ _ _ _ _ _ .

Step-by-step solution

Acceleration can be written as, a = v d v d x . Given: a = - 2 x (-ve sign is due to retardation) Therefore, v d v d x = - 2 x ⇒ v d v = - 2 x d x Integrating both sides, we get 1 2 v f 2 - v i 2 = - 2 x 2 2 = x 2 ⇒ 1 2 m v f 2 - v i 2 = m x 2 ⇒ | Δ K E | = 0 . 01 x 2 = 10 x - 2 Hence, n = 2 .