AP Calculus
PVA (Position, Velocity, & Acceleration)
A particle moves along a horizontal line such that its position at any time t>0 is given by
s(t) = t3 – 6t2 + 9t + 1, where s is measured in meters and t in seconds.
A. Find all times for which the particle is at rest. t = 1, 3
B. Find all times for which the particle changes direction. t = 1, 3
C. Find all times for which the particle is moving left. 1 < t < 3 or (1,3)
D. Find all times for which the velocity is increasing. t > 2
E. Find the total distance the particle travels in the first 2 seconds. 6 units
F. Find the velocity of the particle when the acceleration is 0. v(2) = -3
G. Find all times for which the speed is decreasing. 0 < t < 1 and 2 < t < 3 or (0,1) & (2,3)
*Do it again for s(t) = t3 – 9t2 + 24t
A. t = 2, 4
B. t= 2, 4
C. 2 < t < 4 or (2,4)
D. t > 3
E. 20
F. v(3) = -3
G. 0 < t < 2 and 3 < t < 4 or (0,2) & (3,4)
A particle travels along a horizontal line such that at any time t>0, its velocity is given by
v(t) = 3(t-2)2(t-5) meters per second.
A. At what times, if any, does the particle change direction? t = 5 only
B. Find the acceleration of the particle at any times when it is at rest. a(2) = 0, a(5) = 27