(i)[2]
Show that $\frac{dv}{dt} = 2t - 5e^{-t}$, as required.
(ii)[3]
Using $v = 8$ when $t = 1$, express $v$ in terms of $t$.
(iii)[2]
Find the speed of projection of $P$ from the information given.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
Starting from point O, a particle P of mass 0.4\,\text{kg} is projected horizontally over a smooth horizontal plane. After t\,\text{s}, the velocity of P is v\,\text{m s}^{-1}. A force of magnitude 0.8t\,\text{N} acts away from O, and another force of magnitude 2e^{-t}\,\text{N} acts opposite to the motion of P.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s Second Law to reach $0.4\,\dfrac{dv}{dt} = 0.8t - 2e^{-t}$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI