The force on a particle is given by F(t)= 0.71 t + 1.2 t², in N.If the force acts from t = 0 to t = 2.0 s, the total impulse is: A)1.2 kg∙m/s B)1.9 kg∙m/s C)4.6 kg∙m/s D)4.8 kg∙m/s E)6.2 kg∙m/s

Question

Quizplus · Accepted Answer

Impulse is given by the integral of force over time, $J = \int_{t_1}^{t_2} F(t) \, dt$. Given $F(t) = 0.71t + 1.2t^2$, integrating from $t = 0$ to $t = 2.0$ s gives $J = \left[\frac{0.71}{2}t^2 + \frac{1.2}{3}t^3\right]_0^2 = \left(0.355 \times 4 + 0.4 \times 8\right) = 1.42 + 3.2 = 4.62$ kg∙m/s, which rounds to 4.6 kg∙m/s.

The Force on a Particle Is Given by F(t)= 0