A car of mass 800 kg tows a trailer of mass 200 kg along a straight horizontal road. The engine provides a constant driving force of 3000 N. At speed v v\,v m s−1^{-1}−1, resistance of magnitude 100v 100v\,100v N acts on the car and resistance of magnitude 50v 50v\,50v N acts on the trailer. The tow-bar is light and the car and trailer start from rest.
Show that dvdt=3−0.15v\dfrac{dv}{dt}=3-0.15vdtdv=3−0.15v.
Find v v\,v in terms of ttt.
Find the force in the tow-bar in terms of vvv, and hence find its limiting value.
91 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.