In each of the following cases t ≥ 0. The quantities are given in SI units, so distances are in metres and times in seconds.:

i. Find expressions for the velocity and acceleration at time t

ii. Use these expressions to find the initial position, velocity and acceleration

iii. Find the time and position when the velocity is zero.

a. s = 5t² – t + 3

b. s = 3t – t³

c. s = t⁴ – 4t – 6

d. s = 4t³ – 3t + 5

e. s = 5 – 2t² + t