For a body moving along the -axis

MATHEMATICS · Subjective · A Level · Mathematics · Kinematics · Kinematics

Problem

For a body moving along the

x

-axis, the displacement from the origin at time

t

seconds is

s(t)=t^{4}-6t^{3}+9t^{2}\;\text{(metres)}.

(i) Determine the velocity function

v(t)

. (ii) Find all values of

t

for which the body is at rest. (iii) Identify the intervals of time in the domain

0\le t\le4

during which the body moves to the right and those during which it moves to the left. (iv) Compute the average velocity over the interval

0\text{ s}\le t\le3\text{ s}

and compare it with the instantaneous velocity at

t=3\text{ s}

. Comment briefly on the physical meaning of your result.