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−0.25t x = c + 12t - \lambda e^{-0.25t} x=c+12t−λe−0.25twhere 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.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.