How do a(t), v(t), and x(t) relate in physics equations?

[xpack]

http://img40.imageshack.us/img40/8591/ques.png [/URL]



a(t)=dv/dt
v(t)=dx/dt



I thought it was just
v(t)= ^{(alpha)t^2}/₂ + w
x(t)=^{((alpha)t^2)}/₆ + wt + a

But the answer is ^{((alpha)t^2)}/₆ + wt + a - 2w - ^4(alpha)/₃

Can someone please explain this to me...

 

[Delphi51]

Starting from your v = .5*@*t^2/2 + W
x is the integral dt of this: x = .5*@/3*t^3 + wt + k
To evaluate the constant k, put in time 2 and x = A:
This gives you k = A - 4/3@ - 2w
Put that back in the x formula and you have the answer you are looking for, though there seems to be a t^2 instead of a t^3 in the answer.

 

[xpack]

Thank you very much!