A small 8.00-kg rocket burns fuel that exerts a time- varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation \(F = A + Bt^2\). Measurements show that at t = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants A and B, including their SI units. (b) Find the net force on this rocket and its acceleration (i) the instant after the fuel ignites and (ii) 3.00 s after the fuel ignites. (c) Suppose that you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition?

Step 1 of 4

(a) Find the constants A and B, including their SI units.

F = A+B

By substituting t= 0 and F=100 N in the given equation,

100 N= A+B(0)

A= 100 N

By substituting A= 100 N, t= 2s and F= 150 N

150 N= 100N+B(2 s)

B= 12.5 N.

Using above results given equation becomes,

F= 100+ 12.5…………..1