Originally Posted by alex34 I need help with all the following and will post under each what I believe the answer is. Thank you in advance!
A body of mass m accelerates uniformly from rest to a speed of V in total time T.
(a) Mathematically derive an equation for the work done on the body as a function of time T.
W= ∫FD and F=ma > F=m(dv/dt) so ∫F(t)/m dt ? 
No, with F= m(dv/dt), F(m)= (dv/dt) so ∫F(t)/m dt= ∫(dv/dt)dt= ∫dv= v. that gives v, not W.
Your "W= ∫FD" should be "W= ∫F dx". Then v= dx/dt so that dx= vdt. That can be written as "W= ∫ F v dt". Now, with F= ma= m(dv/dt) "W= ∫F v dt= ∫m(dv/dt) v dt= ∫mv dv. For constant m, that is (1/2)mv^2.
(b)Now derive an equation for instantaneous power delivered to the object
Power = work/time not really sure where to go for this one.

"Power= work/time" only for constant work and time. More generally, power= the derivative of work with respect to time.
(c) Calculate the power at the end of 5sec delivered to a body of 1500N which accelerates 2m/s in 10s.
½mv²= KE = work P= work/ 20
again, not really sure. Any help appreciated

How fast was the energy being delivered to the body at t= 5 sec?