The displacement of a particle is described by (SI units)

MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics

Problem

The displacement of a particle is described by

x(t) = t^{3} - 6 t^{2} + 9 t + 4

(SI units). Let

v_{1}, v_{2}

and

v_{3}

denote the instantaneous velocities at

t = 1\,\text{s}

2\,\text{s}

and

4\,\text{s}

respectively. Which of the following correctly lists them in ascending order? (a)

v_{3} < v_{2} < v_{1}

(b)

v_{2} < v_{3} < v_{1}

(c)

v_{2} < v_{1} < v_{3}

(d)

v_{1} < v_{2} < v_{3}