Question

At time t second, a particle of mass 3 kg has position vector $\overset{\rightarrow}{r}$ metre, where $\overset{\rightarrow}{r} = 3t\widehat{i} - 4\cos t\widehat{j}.$ The impulse of the force during the time interval $0 \leq t \leq \frac{\pi}{2}$ is –

• A. $12\widehat{j}Ns$
• B. $9\widehat{j}Ns$
• C. $4\widehat{j}Ns$
• D. $14\widehat{j}Ns$

Answer 1

Answer: (A)

$12\widehat{j}Ns$

Answer 2

Given that $\vec { r } = 3 t \hat { i } - 4 \cos t \hat { j }$ $\frac{d\overset{\rightarrow}{r}}{dt} = 3\widehat{i} + 4\sin t\widehat{j}$

Ž$\frac{d^{2}\overset{\rightarrow}{r}}{dt^{2}} = + 4\cos t\widehat{j}$

Impulse = $\int_{}^{}{\overset{\rightarrow}{F} \cdot dt = \int_{0}^{\pi/2}{m\overset{\rightarrow}{a}}dt =}\int_{0}^{\pi/2}m(4\cos t\widehat{j}) \cdot dt$

=$\widehat{i}\int_{0}^{\pi/2}12\cos t \cdot dt = 12\widehat{j}N \cdot S$