A small 6.10-kg rocket burns fuel that exerts a time-varying upward force on the

Question

A small 6.10-kg rocket burns fuel that exerts a time-varying upward force on the rocket. This force obeys the equation F=A+Bt2. Measurements show that at t=0, the force is 126.0N , and at the end of the first 2.50s , it is 150.0N .

A.Find the net force on this rocket the instant after the fuel ignites.

B.Find the acceleration of this rocket the instant after the fuel ignites.

C.Find the net force on this rocket 4.00s after fuel ignition.

D.Find the acceleration of this rocket 4.00s after fuel ignition.

E.Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 4.00s after fuel ignition?

Explanation / Answer

Given that

At t = 0 , F = A = 126 N

At t = 2.5 s, F = A + Bt2 = 150 N

==> 126 N + B * 2.5 * 2.5 = 150 N

==> B = 3.84 N

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(a) Immediately after fuel ignites, F = 126 N, as t = 0 s

(b) a = F /m = 126 / 6.10 = 20.65 m/s2

(c) when t = 4 s,

F = 126 + 3.84 * 16

= 187.44 N

(d) At t = 4s,

a = 187.44 / 6.10 = 30.72 m/s2

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