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 = F0 [1 - ((t - T)/T)²]
Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after ti

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 = F0 [1 - ((t - T)/T)²]
Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:

Accepted Answer

4F0T/3M. The correct option is derived from integrating the force over the time interval to find the impulse, which gives the change in momentum. The force function is a quadratic function of time, and when integrated from 0 to 2T, it results in a total impulse that leads to a final velocity of 4F0T/3M.

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 = F0 [1 - ((t - T)/T)²] Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:

Solution

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