A particle P P\,P travels along a straight line through a point O O\,O so that at time t t\,t s after passing through O O\,O its displacement from O O\,O is x x\,x m. Its velocity is v v\,v m s−1^{-1}−1, where v=16t3−12t2+2tv = 16t^3 - 12t^2 + 2tv=16t3−12t2+2t.
Find the displacement x x\,x of P P\,P in terms of ttt.
Show that P P\,P will never move along the negative xxx-axis.
Find the total distance travelled by P P\,P in the interval 0≤t≤50 \leq t \leq 50≤t≤5
308 exam-style questions on Edexcel A Level Maths Variable Acceleration, covering 11.1 Functions of Time, 11.2 Using Differentiation, 11.3 Maxima and Minima Problems, 11.4 Using Integration, and 11.5 Constant Acceleration Formulae. Each one has a worked solution and a mark scheme showing where the marks go.