A particle of mass m 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 charges from p to 3p. Here k is a constant. The value of T is

Engineering

Physics

Momentum and Energy Conservation for System of Particles

Newtons Second Law of Motion

Question

A particle of mass m 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 charges from p to 3p. Here k is a constant. The value of T is

$2 \sqrt{\frac{p}{k}}$

$\sqrt{\frac{2 k}{p}}$

$2 \sqrt{\frac{k}{p}}$

$\sqrt{\frac{2 p}{k}}$

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$\frac{dp}{dt} = F = kt$

$\int_{P}^{3 P} dp = \int_{0}^{T} kt dp$

$2 p = \frac{{KT}^{2}}{2}; T = 2 \sqrt{\frac{p}{k}}$