A particle moves such that its velocity is given by (in m/s).

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves such that its velocity is given by

v(t)=8t-2t^{2}+\dfrac{t^{3}}{6}

(in m/s). (i) Derive an expression for its instantaneous acceleration

a(t)

. (ii) Find the time within the first

5\,\text{s}

when the acceleration is zero. (iii) Calculate the speed of the particle at that instant.