A particle’s position is defined by s(t)= cases t^ 2 +1, & t 3, 6t-8, & t>3
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A particle’s position is defined by
s(t)={t2+1,6t−8,t≤3,t>3.
Which of the following statements about the particle’s instantaneous velocity at t=3 seconds is correct?
(a) The instantaneous velocity exists and equals 10units/s.
(b) The instantaneous velocity exists and equals 6units/s.
(c) The instantaneous velocity does not exist because the velocities from the left and right differ.
(d) The instantaneous velocity exists and equals 3units/s.