A particle moves in a straight line through the origin OOO.
The displacement of the particle, r r\,r metres, from O O\,O at time t t\,t seconds is given by r=p+3t−qe−0.25tr = p + 3t - q\mathrm{e}^{-0.25t}r=p+3t−qe−0.25t where p p\,p and q q\,q are constants.
When t=4t = 4t=4, the acceleration of the particle is -1.5 m s−2^{-2}−2.
Show that q≈65q \approx 65q≈65.
The particle has an initial displacement of 8 metres. Find the value of ppp, giving your answer to two significant figures.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.