3.100: Particle with logarithmic displacement

0606/22/F/M/25 — Question 9 · 11 marks

In this question, all lengths are in metres and time is in seconds.
A particle PP moves in a straight line such that tt seconds after passing through a fixed point OO its displacement ss is given by
s=5ln(2t+1)5t.s = 5\ln(2t + 1) - 5t.
(a)
Find the value of tt for which PP is instantaneously at rest.
[4]
(b)
Find the distance PP travels between t=0t = 0 and t=2t = 2.
[4]
(c)
Find an expression for the acceleration of PP in terms of tt.
[2]
(d)
Find the acceleration when t=4.5t = 4.5.
[1]