Question

A particle with linear momentum of magnitude P is subjected to a force F= Kt (k > 0) which is directed along the directed of initial momentum. The time which its liner momentum changes to 3P is :

• A. $\sqrt{\frac{2P}{K}}$
• B. $2\sqrt{\frac{P}{K}}$
• C. $\sqrt{\frac{2K}{P}}$
• D. $2\sqrt{\frac{K}{P}}$

Answer 1

The correct option is B $2\sqrt{\frac{P}{K}}$

Impulse is $dP=Fdt$

integrating both sides we get ${\int }_P^{3P}dP={\int }_{t=0}^{t}Ktdt$

or $2P=\frac{K{t}^2}{2}$ so $t=\sqrt{\frac{4P}{K}}$