At time t=0 a 2150 kg rocket in outer space fires an engine that exerts an increasing force on it in the +x−direction. This force obeys the equation Fx=At2, where t is time, and has a magnitude of 888.93 N when t=1.25 s.

a) What impulse does the engine exert on the rocket during the 4.0 s interval starting 2.00 s after the engine is fired?
b) By how much does the rockets velocity change during this interval?
c) Find the SI value of the constant A, including its units.

Explanation:

Given that,

Mass of the rocket, m = 2150 kg

At time t=0 a rocket in outer space fires an engine that exerts an increasing force on it in the +x−direction. The force is given by equation :

Here F = 888.93 N when t = 1.25 s

(c) We can find the value of A first as :

The value of A is .

(a) Let J is the impulse does the engine exert on the rocket during the 4.0 s interval starting 2.00 s after the engine is fired. It is given in terms of force as :

Limits will be from 2 s to 2+ 4 = 6 s

It implies :

(b) Impulse is also equal to the change in momentum as :

Hence, this is the required solution.

we need to know the time interval during which the force acts. impulse of force = momentum change