3.108: Particle with $\mathrm{ln}$ displacement

0606/23/O/N/23 — Question 6 · 9 marks

A particle travels in a straight line. Its displacement,

s

metres, from the origin at time

t

seconds, where

t \geqslant 2

, is given by

s = \mathrm{ln}(4t^{2} - 5) - t

(a)

Find expressions for the velocity,

v\,\mathrm{ms}^{-1}

, and acceleration,

a\,\mathrm{ms}^{-2}

, of the particle.

[4]

(b)

Find the time when the particle is at rest.

[3]

(c)

Find the acceleration at this time.

[2]

3.108: Particle with ln\mathrm{ln}ln displacement