For a particle moving along a straight line

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

Problem

For a particle moving along a straight line, its displacement as a function of time is given by

x(t)=3t^{2}-6t+2\quad (x\text{ in m},\; t\text{ in s}).

Answer the following questions. (a) Write the mathematical expression that gives the instantaneous velocity of the particle in terms of

t

. Clearly state the physical meaning of each symbol used. (b) Calculate the instantaneous velocity of the particle at

t = 1.5\,\text{s}

. (c) Determine the average velocity of the particle during the short time interval from

t = 1.4\,\text{s}

t = 1.6\,\text{s}

. Compare this value with the result obtained in part (b) and comment briefly on the closeness of the two values.