Mathematics

Problem

A body moves along a straight line so that its displacement from the origin at time

t

seconds is given by

s(t)=2t^{4}-5t^{3}+3t^{2}-7t+10\;\text{metres}.

Answer the following: a. (i) Find the expressions for the velocity

v(t)

and the acceleration

a(t)

of the body. b. (ii) Determine the values of velocity and acceleration at

t=2\,\text{s}

. c. (iii) Find the value(s) of

t

for which the acceleration becomes zero. State the corresponding velocity at that instant.