A particle moves in a straight line relative to an origin OOO. The displacement, sss metres, of the particle from OOO at time ttt seconds is given by
s=p+5t−ke−0.4t s = p + 5t - ke^{-0.4t} s=p+5t−ke−0.4twhere ppp and kkk are constants. At time t=2t = 2t=2, the acceleration of the particle is −2.4 m s−2-2.4\text{ m s}^{-2}−2.4 m s−2.
Show that k≈33.4k \approx 33.4k≈33.4
Given that the particle has an initial displacement of 8 metres, find the value of ppp. Give 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.