Additional Mathematics 4037: Calculus Topical Past Paper Questions

In this question the units are metres and seconds. A particle moves along a straight line through a point A. Its displacement, $s$, from $A$ at time $t$ is given by $s=\frac{10t+100}{\sqrt{2t^{2}+100}}$. The diagram shows the displacement-time graph for the first 30 seconds of th…

A particle moves in a straight line. Its velocity, $v \mathrm{~m s}^{-1}$, at time $t$ seconds is given by $$ \gamma=\cos t-\sin t. $$ (a) Find the acceleration, $ a \, \mathrm{ms}^{-2} $, when $ t = \frac{\pi}{3} $ [2] The displacement of the particle from a fixed point O at tim…

A curve has equation $ y = xe^{2x} $. (a) Find $ \frac{dy}{dx} $. [2] (b) Find the equation of the normal to the curve at x=1. [4] (c) Use your answer to part (a) to find the exact value of $ \int_{0}^{2}2xe^{2x}dx $. [5]