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.
