Far in space, where gravity is negligible, a 465 kg rocket traveling at 75.0 m/s in the positive x-direction fires its engines. The figure (Figure 1)shows the thrust force as a function of time. The mass lost by the rocket during these 30.0 s is negligible.

In classical mechanics, the integral of a force, F, over the time period over which it acts, t, is known as the impulse (abbreviated J or Imp).
Impulse is a vector quantity because force is one as well. When an item receives an impulse, its linear momentum also changes in the opposite direction in an analogous vector. The kilogram meter per second (kg m/s), which is dimensionally identical to the kilogram second (Ns), is the SI unit for momentum.
For as long as it acts, a resultant force generates acceleration and a change in the body's velocity. The change in momentum is equal to the product of the average force and duration, hence a resultant force delivered over a longer period of time results in a greater change in linear momentum than a resultant force applied quickly.

Solution:

Mass of the rocket = 465kg

Velocity of the rocket = 75m/s

Time taken = 30s

Impulse = [tex]I = F \Delta t[/tex]

[tex]I = \int F(t)dt[/tex]

Impulse so generated is equal to the area of triangle

I = [tex]\frac{1}{2} \times 30\times1000[/tex]

I = 15000 Ns

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