A car of mass 1000 kg moves along a horizontal road. Its engine provides a constant driving force of 4000 N. At speed v v\,v m s−1^{-1}−1 the resistance to motion is 500v 500v\,500v N. The car starts from rest.
Show that dvdt=4−0.5v\dfrac{dv}{dt}=4-0.5vdtdv=4−0.5v.
Find v v\,v in terms of ttt.
Find the time taken for the speed to reach 6 m s−1^{-1}−1.
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.