3.110: Trigonometric velocity; acceleration and displacement

0606/21/O/N/23 — Question 7 · 10 marks

(a)

A particle has velocity

v=10\sin 2t-6\cos 2t\,\mathrm{ms}^{-1}

. Find an expression for the acceleration.

[2]

(b)

Find the acceleration when

t=\dfrac{\pi}{4}

[1]

(c)

Find the first time at which the acceleration is zero.

[3]

(d)

Find the displacement of the particle between

t=\dfrac{\pi}{4}

and

t=\dfrac{\pi}{2}

[4]