A body moves along a straight line with displacement (metres)

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A body moves along a straight line with displacement

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

(metres). Let

v_{1}

and

v_{5}

be its instantaneous velocities at

t = 1\,\text{s}

and

t = 5\,\text{s}

respectively. Which option is correct? (a)

v_{1}=-6\,\text{m s}^{-1}

v_{5}=18\,\text{m s}^{-1}

(b)

v_{1}=0\,\text{m s}^{-1}

v_{5}=24\,\text{m s}^{-1}

(c)

v_{1}=0\,\text{m s}^{-1}

v_{5}=15\,\text{m s}^{-1}

(d)

v_{1}=4\,\text{m s}^{-1}

v_{5}=20\,\text{m s}^{-1}