Penny - it should be
v = t^3 + 2t^2 + 7t + c
You forgot the 7 as the coefficient for t^1
As the velocity is 8940, the air resistance is 8940 N
Newton's 2nd Law:
F = ma
Using the equation a = 3t^2 + 4t +7
a = 1287 m/s^2
F = 65 x 1287
= 83655 N
Summing the forces,
F (total) = 83655 - 8940
And I get to do stuff like that everyday!!! Yay for engineering!
Now...would you like a harder one???