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−0.4ts = p + 5t - ke^{-0.4t}s=p+5t−ke−0.4t
where 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.
Practise Edexcel A Level Maths Further Kinematics with exam-style questions for A Level Maths. 54 questions covering Vectors in Kinematics, Vector Methods with Projectiles, Variable Acceleration in One Dimension, Differentiating Vectors, and Integrating Vectors, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.