A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F 0 1 - t - T T 2 where F 0 and T are constants. The force acts only for the time interval 2 T . The velocity v of the particle after time 2 T is:

Question

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F 0 1 - t - T T 2 where F 0 and T are constants. The force acts only for the time interval 2 T . The velocity v of the particle after time 2 T is:, 2 F 0 T M, F 0 T 2 M, 4 F 0 T 3 M, F 0 T 3 M

MARKS App · Accepted Answer

t = 0 , u = 0 a = F o M - F o M T 2 ( t - T ) 2 = d v d t ∫ 0 v d v = ∫ t = 0 2 T F o M - F o M T 2 ( t - T ) 2 d t V = F o M t o 2 T - F o M T 2 t 3 3 - t 2 T + T 2 t 0 2 T V = 4 F o T 3 M

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