A particle moves along a straight line so that its position (in meters) at time…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A particle moves along a straight line so that its position (in meters) at time t seconds is given by s(t)=t+2t for t≥0.
(a) Set up the limit expression that represents the instantaneous velocity v(t) of the particle at a general time t. Do not evaluate the limit yet.
(b) Evaluate the limit from part (a) to derive an explicit formula for v(t) for all admissible t. Show each algebraic step of your work.
(c) Compute the instantaneous velocity at t=3 seconds and state its units.
(d) Discuss whether the particle's velocity ever becomes zero for t≥0. Justify your answer using the formula found in part (b).