Answer
(a) $A = 500~N/s^2$
(b) The rocket exerts an impulse of 5810 kg m/s.
(c) The velocity changes by 2.70 m/s.
Work Step by Step
(a) When t = 1.25 s:
$At^2 = 781.25~N$
$A = \frac{781.25~N}{t^2}$
$A = \frac{781.25~N}{(1.25~s)^2}$
$A = 500~N/s^2$
(b) $J = \int_{2.00}^{3.50}F~dt$
$J = \int_{2.00}^{3.50}At^2~dt$
$J = \frac{A}{3}t^3\vert_{2.00}^{3.50}$
$J = \frac{(500~N/s^2)}{3}[(3.50~s)^3 - (2.00~s)^3]$
$J = 5810~kg~m/s$
The rocket exerts an impulse of 5810 kg m/s.
(c) $\Delta p = J$
$m \Delta v = J$
$\Delta v = \frac{J}{m} = \frac{5810~kg~m/s}{2150~kg}$
$\Delta v = 2.70~m/s$
The velocity changes by 2.70 m/s.
