1.78: Exponential displacement, velocity and acceleration

0606/13/O/N/18 — Question 6 · 9 marks

A particle PP is moving in a straight line such that its displacement, ss m, from a fixed point OO at time tt s, is given by s=12e0.5t+4t12s = 12\mathrm{e}^{-0.5t} + 4t - 12.
(i)
Find the value of tt when PP is instantaneously at rest.
[3]
(ii)
Find an expression for the acceleration of PP at time tt s.
[2]
(iii)
Find the value of ss when the acceleration of PP is 0.30.3 m s2^{-2}.
[3]
(iv)
Explain why the acceleration of the particle will always be positive.
[1]