Two cyclists start together along a straight road

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

Problem

Two cyclists start together along a straight road. Their displacements (in metres) after

t

seconds are Cyclist A:

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

, Cyclist B:

s_B(t)=t^{2}-2t+4

. At what smallest positive time will they have the same instantaneous velocity? (a)

2\,\text{s}

(b)

1\,\text{s}

(c)

\dfrac{11}{3}\,\text{s}

(d)

0.5\,\text{s}