A particle of mass is acted upon by a force for and by no force afterwards

MATHEMATICS · Subjective · A Level · Mathematics · Forces and Newton's laws · Forces and Newton's laws

Problem

A particle of mass

m

is acted upon by a force

F(t)=F_0\sin\!\left(\dfrac{\pi t}{T}\right)

for

0\le t\le T

and by no force afterwards. The particle starts from rest. Derive an expression for its speed immediately after

t=T

in terms of

F_0

T

and

m