A parcel slides down a rough plane inclined at an angle α \alpha\,α to the horizontal, where sinα=513\displaystyle \sin\alpha=\frac5{13}sinα=135. The coefficient of friction is 14\displaystyle \frac1441. In addition to friction, a resistive force of magnitude 2mv 2mv\,2mv N acts up the plane, where m m\,m kg is the mass of the parcel and v v\,v m s−1^{-1}−1 is its speed. The parcel starts from rest.
Show that dvdt=2g13−2v\dfrac{dv}{dt}=\dfrac{2g}{13}-2vdtdv=132g−2v.
Find v v\,v in terms of t t\,t and ggg.
Determine whether the speed can exceed 1 m s−1^{-1}−1 when g=9.8g=9.8g=9.8 m s−2^{-2}−2.
92 exam-style questions on WJEC A Level Maths 4.6 Integration (A-level only), covering 4.6.1 Integration (A-level only) and 4.6.2 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.