1.32: Simple harmonic motion of a particle

0606/12/M/J/17 — Question 5 · 6 marks

A particle

P

moves in a straight line, such that its displacement,

x

m, from a fixed point

O

t

s after passing

O

, is given by

x = 4\cos 3t - 4

(i)

Find the velocity of

P

at time

t

[1]

(ii)

Hence write down the maximum speed of

P

[1]

(iii)

Find the smallest value of

t

for which the acceleration of

P

is zero.

[3]

(iv)

For the value of

t

found in part (iii), find the distance of

P

from

O

[1]