Question

The velocity of a particle is v=v0[1-sin(xt/T)]. Knowing that the particle starts from the origin with an initial velocity vo, determine (a) its position and its acceleration at t = 3T, (b) its average velocity during the interval t = 0 to t = T.

Answer 1

$a(T)=v'=-\frac{\pi}T v_0\cos\frac{\pi t}T,$

$a(3T)=\frac{\pi v_0}T .$

$<v>=\frac{\int_0^Tvdt}T=v_0(1-\frac 2{\pi}).$