1.34: Logarithmic displacement, velocity and acceleration

0606/12/M/J/18 — Question 4 · 7 marks

A particle PP moves so that its displacement, xx metres from a fixed point OO, at time tt seconds, is given by x=ln(5t+3)x = \ln(5t + 3).
(i)
Find the value of tt when the displacement of PP is 33 m.
[2]
(ii)
Find the velocity of PP when t=0t = 0.
[2]
(iii)
Explain why, after passing through OO, the velocity of PP is never negative.
[1]
(iv)
Find the acceleration of PP when t=0t = 0.
[2]