Mathematics A H230: Integration Topical Past Paper Questions

A man P runs in a straight line from O to A, leaving O at time t = 0. At time t seconds his velocity $ v_{ms}^{-1} $ is given by $ v = 5 + 0.003t^{2} $. Another man $Q$ runs from $O$ to $A$ at a constant speed of $7.08\,\mathrm{m\,s}^{-1}$, starting 5 seconds after $P$. (a) Show…

A particle P is moving in a straight line. At time t seconds, where $ t \geqslant 0 $, P has velocity $ v \, m \, s^{-1} $ and acceleration $ a \, m \, s^{-2} $ where a = 4t-9. It is given that v = 2 when t = 1. (a) Find an expression for v in terms of t. [3] The particle $P$ is…

The diagram shows the curve $y = 1 - x + \frac{6}{\sqrt{x}}$ and the line $l$, which is the normal to the curve at the point $(1, 6)$. (a) Determine the equation of $l$ in the form $$ ax+by=c $$ where $a$, $b$ and $c$ are integers whose values are to be stated. [5] (b) Verify tha…