A particle of mass m, initially at rest at x=0, is accelerated by a force that increases in time as f=ct2. Determine its velocity v and position x as a function of time.
a) v(t) = ct3/3m, x(t) = ct4/12m
b) v(t) = ct3/3m, x(t) = ct4/4m
c) v(t) = ct2/2m, x(t) = ct3/3m
d) v(t) = ct2/2m, x(t) = ct3/12m
