A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0 , a force F = k t acts in the same direction on the moving particle during time interval T so that its momentu

Question

A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0 , a force F = k t acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3 p . Here k is a constant. The value of T is

TestHub · Accepted Answer

From Newton's second law dt dp ​ = F = kt Integrating both sides we get, ∫ p 3 p ​ dp = ∫ 0 T ​ ktdt ⇒ [ p ] p 3 p ​ = k [ 2 t 2 ​ ] 0 T ​ ⇒ 2 p = 2 kT 2 ​ ⇒ T = 2 k p ​ ​

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