Answer:
[tex]Imp = 5626.488\,\frac{kg\cdot m}{s}[/tex]
Explanation:
First, it is required to model the function that models the increasing force in the +x direction:
[tex]a =\frac{781..25\,N}{(1.27\,s)^{2}}[/tex]
[tex]a = 484 \frac{N}{s^{2}}[/tex]
The equation is:
[tex]F_{x} = 484\,\frac{N}{s^{2}}\cdot t^{2}[/tex]
The impulse done by the engine is given by the following integral:
[tex]Imp=484\,\frac{N}{s^{2}} \int\limits^{3.50\,s}_{2\,s} {t^{2}} \, dt[/tex]
[tex]Imp = 161.333\,\frac{N}{s^{2}}\cdot [(3.50\,s)^{3}-(2\,s)^{3}][/tex]
[tex]Imp = 5626.488\,\frac{kg\cdot m}{s}[/tex]
