A high-precision hydraulic piston moves in a straight line inside a cylinder relative to a reference marker MMM. The displacement, x x\,x metres, of the piston from M M\,M at time t t\,t seconds is given by
x=c+12t−λe−0.25tx = c + 12t - \lambda e^{-0.25t}x=c+12t−λe−0.25t
where c c\,c and λ \lambda\,λ are constants. At time t=4t = 4t=4, the acceleration of the piston is -1.5 m s-2.
Show that λ≈65.2\lambda \approx 65.2λ≈65.2
Given that the piston has an initial displacement of 16 metres, find the value of ccc. 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.