Question

The force on a particle of mass m is given by F⃗ =26iˆ−13t2jˆ where F is in N and t in s. What will be the change in the particle's momentum between t = 1.0 s and t = 4.0 s ?

Answer 1

Force $\vec{F}=26\hat{i}-13t^2\hat{j}$

Newton's second law

$\vec{F}=\frac{d\vec{p}}{dt}$

$d\vec{p}=\vec{F}dt$

$\vec{p}=\int \vec{F}dt$

$\vec{p}=\int_{1}^{4} (26\hat{i}-13t^2\hat{j})dt$

$\vec{p}=\left [ (26t\hat{i}-13t^3/3\hat{j}) \right ]_{1.0}^{4.0}$

$\vec{p}= (78\hat{i}-117\hat{j})kgm/s$