A particle moves along a straight line with position function p(t)=|t-4|, 0 t 8
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A particle moves along a straight line with position function
p(t)=∣t−4∣,0≤t≤8,
where t is measured in seconds and p(t) in meters.
(a) Determine whether p is continuous at t=4. Provide a justification based on limits.
(b) Compute the left–hand and right–hand derivatives of p at t=4, or show that one or both of these one–sided derivatives do not exist.
(c) Based on your results from part (b), state whether the instantaneous velocity of the particle exists at t=4 and interpret your conclusion within the context of the particle’s motion.