The height (in metres) of a piston moving up and down in an engine cylinder after…

MATHEMATICS · Subjective · A Level · Mathematics · Kinematics · Kinematics

Problem

The height (in metres) of a piston moving up and down in an engine cylinder after

t

seconds is modelled by

s(t)=5\sin\left(\tfrac{\pi t}{4}\right)+10.

(i) Obtain the velocity function

v(t)

. (ii) Find the velocity of the piston at

t=2\text{ s}

and at

t=6\text{ s}

. (iii) State, with reasons, whether the piston is moving upward or downward at each of these instants.