Question

a force changes the velocity of a body of mass 10kg from 5m/s to 20m/s in 2 seconds. Find a) the initial momentum of the body b) the final momentum of the body c) the change in momentum of the body and d) the force acting on the body

Answer 1

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{a}\mathrm{body}:\mathrm{m}=10\mathrm{kg} \\ \mathrm{Initial}\mathrm{velocity}:\mathrm{u}=5\mathrm{m}/\mathrm{s} \\ \mathrm{Final}\mathrm{velocity}:\mathrm{v}=20\mathrm{m}/\mathrm{s} \\ \left(\mathrm{a}\right) \\ \mathrm{Initial}\mathrm{momentum}: \\ {\mathrm{p}}_1=\mathrm{mu} \\ =10\times 5 \\ =50\mathrm{kg}·\mathrm{m}/\mathrm{s} \\ \left(\mathrm{b}\right) \\ \mathrm{Final}\mathrm{momentum}: \\ {\mathrm{p}}_2=\mathrm{mv} \\ =10\times 20 \\ =200\mathrm{kg}·\mathrm{m}/\mathrm{s} \\ \left(\mathrm{c}\right) \\ \mathrm{Change}\mathrm{in}\mathrm{momentum}: \\ △\mathrm{p}={\mathrm{p}}_2-{\mathrm{p}}_1 \\ =200-50 \\ =150\mathrm{kg}·\mathrm{m}/\mathrm{s} \\ \left(\mathrm{d}\right) \\ \mathrm{Force}: \\ \mathrm{F}=\frac{△\mathrm{p}}{△\mathrm{t}} \\ =\frac{150}{2} \\ =75\mathrm{N} \end{gathered}$$