Mathematics

Problem

The displacement of a particle moving along a straight line at time

t

seconds is given by

s(t) = \sqrt{2t^2 + 3t + 1}

metres. a. (i) Obtain expressions for the velocity

v(t)

and acceleration

a(t)

of the particle. b. (ii) Calculate the acceleration of the particle at

t = 2\,\text{s}

, leaving your answer in simplest form.