2.64: Kinematics with displacement $5t + \sin t$

0606/23/M/J/19 — Question 11 · 8 marks

A particle travelling in a straight line passes through a fixed point

O

. The displacement,

x

metres, of the particle,

t

seconds after it passes through

O

, is given by

x = 5t + \sin t

(i)

Show that the particle is never at rest.

[2]

(ii)

Find the distance travelled by the particle between

t = \dfrac{\pi}{3}

and

t = \dfrac{\pi}{2}

[2]

(iii)

Find the acceleration of the particle when

t = 4

[2]

(iv)

Find the value of

t

when the velocity of the particle is first at its minimum.

[2]

2.64: Kinematics with displacement 5t+sin⁡t5t + \sin t5t+sint