Question

A particle moves in a straight line with retardation proportional to displacement. Its loss of kinetic energy for any displacement x proportional to ............. .
(A) x²
(B) eˣ
(C) x
(D) log eˣ

Answer 1

Dear Student,

● Answer - (A)

∆KE ∝ x²

◆ Explanation -

Given that,

a ∝ x

a = -k.x

Substitute a = v.dv/dx,

v.dv/dx = -k.x

v.dv = kx.dx

Integrating both sides,

ʃv.dv = ʃkx.dx

(v2²-v1²)/2 = -kx²/2

Change in kinetic energy of the particle is -

∆KE = m(v2²-v1²)/2

∆KE = -mkx²/2

∆KE ∝ x²

Therefore, loss of kinetic energy of the particle is directly proportional to x².

Thanks dear...