A particle moves along the -axis according to metres.

MATHEMATICS · Multi-part · A Level · Mathematics · Kinematics · Kinematics

Problem

A particle moves along the

x

-axis according to

x(t)=6t^{3}-9t^{2}+2

metres. (i) Find the average velocity of the particle between

t=1\,\text{s}

and

t=3\,\text{s}

. (ii) Obtain an expression for the instantaneous velocity

v(t)

. (iii) Prove that there exists a time

t_{0}

in the interval

1\,\text{s}<t<3\,\text{s}

at which the instantaneous velocity equals the average velocity found in part (i). (iv) Calculate the exact value of

t_{0}