1.64: Particle kinematics with trigonometric velocity

0606/13/M/J/17 — Question 12 · 9 marks

A particle moves in a straight line, such that its velocity,

v

m s

^{-1}

t

s after passing a fixed point

O

, is given by

v = 2 + 6t + 3\sin 2t

(i)

Find the acceleration of the particle at time

t

[2]

(ii)

Hence find the smallest value of

t

for which the acceleration of the particle is zero.

[2]

(iii)

Find the displacement,

x

m from

O

, of the particle at time

t

[5]