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

Options

A. `sqrt((2p)/(k))`
B. `2sqrt(k/p)`
C. `sqrt((2k)/(p))`
D. `2sqrt(p/k)`

Answer

D

Explanation

`(dvecP)/(dt) = vecF , dvecP = vecF dt, " "DeltavecP = int vecF dt`
`:. 3 P - P = int_(0)^(T) k tdt , " "2P = (KT^2)/(2) , " " T = 2sqrt(P/K)`.