Question

"At time t = 0 a 2330-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 781.25 N when t = 1.27 s .
What impulse does the engine exert on the rocket during the 1.50- s interval starting 2.00 s after the engine is fired?

Answer 1

Answer:

$Imp = 5626.488\,\frac{kg\cdot m}{s}$

Explanation:

First, it is required to model the function that models the increasing force in the +x direction:

$a =\frac{781..25\,N}{(1.27\,s)^{2}}$

$a = 484 \frac{N}{s^{2}}$

The equation is:

$F_{x} = 484\,\frac{N}{s^{2}}\cdot t^{2}$

The impulse done by the engine is given by the following integral:

$Imp=484\,\frac{N}{s^{2}} \int\limits^{3.50\,s}_{2\,s} {t^{2}} \, dt$

$Imp = 161.333\,\frac{N}{s^{2}}\cdot [(3.50\,s)^{3}-(2\,s)^{3}]$

$Imp = 5626.488\,\frac{kg\cdot m}{s}$