3.40: Kinematics with sine velocity

0606/11/M/J/24 — Question 10 · 9 marks

In this question, all distances are in metres and time,

t

, is in seconds.

A particle

P

is at a fixed point

O

at time

t=0

. The velocity,

v

, of

P

is given by

v=3\,\mathrm{sin}\,2t

for

t\geqslant 0

(a)

Find the exact value of

t

for which the velocity is zero for the first time after

P

leaves

O

[2]

(b)

Find an expression, in terms of

t

, for the displacement of

P

from

O

at time

t

[4]

(c)

Find the distance travelled by

P

for

0\leqslant t\leqslant \pi

[3]