A particle moves along the -axis such that its position as a function of time is

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

Problem

A particle moves along the

x

-axis such that its position as a function of time is

x(t) = 4t^{2} - 2t^{3} + 10

, where

x

is in metres and

t

in seconds. (i) Obtain an expression for the instantaneous velocity

v(t)

of the particle. (ii) Calculate the instantaneous velocity at

t = 1\,\text{s}

and at

t = 3\,\text{s}

. (iii) Find the average velocity of the particle during the interval

t = 1\,\text{s}

t = 3\,\text{s}

. (iv) Determine the instantaneous speed at

t = 3\,\text{s}

. (v) Comment briefly on the relation between the average velocity obtained in part (iii) and the instantaneous velocities found in part (ii).