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

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A body of mass m is moving in a straight line with momentum p . Starting at time t = 0 , a force F = a t acts in the same direction on the moving particle during time interval of T . So that its momentum changes from p to 2 p . The value of T is

TestHub · Accepted Answer

Given, F = a t when, t = 0 , then linear momentum = p when, t = T , then linear momentum = 2 p According to Newton's law of motion, applied force, F = d p d t or d p = F d t d p = a t d t or ∫ p 2 p d p = a ∫ 0 T t d t 2 p - p = a · T 2 2 ⇒ 2 p a = T 2 ⇒ T = 2 p a

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