3.109: Particle with exponential displacement

0606/22/O/N/23 — Question 7 · 9 marks

(a)
A particle has displacement s=32t+2et−e−2ts=\dfrac{3}{2}t+2e^{t}-e^{-2t}. Find expressions for the velocity and acceleration.
[3]
(b)
Find the time TT when the particle is at rest.
[4]
(c)
Find the acceleration at time TT.
[2]