A particle moves along a straight line with velocity (in meters per second) for seconds
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a straight line with velocity v(t)=t2−4t (in meters per second) for 0≤t≤6 seconds, where positive velocity corresponds to motion to the right.
(a) Determine all times in [0,6] at which the particle changes direction.
(b) Compute the total distance traveled by the particle during the time interval 0≤t≤6 seconds.
(c) Find the particle’s net displacement over the interval 0≤t≤6 seconds and compare it to the total distance found in part (b).
(d) The particle’s acceleration is a(t)=2t−4. Decide whether the particle’s speed is increasing or decreasing at t=1 and at t=5, and provide justification for each time.