86 Part I: The Questions
Finding the Distance Traveled
by a Particle Given
Acceleration
633–635 A particle moves according to the given
acceleration function over the given interval.
Find the total distance traveled by the particle.
Remember: Displacement is the change in position,
velocity is the rate of change in position with respect
to time, and acceleration is the rate of change in
velocity with respect to time.
633. a(t) = t + 2, v
 
(0) = –6, 0 ≤ t ≤ 8
634. a(t) = 2t + 1, v
 
(0) = –12, 0 ≤ t ≤ 5
635. a(t) = sin t + cos t, v π
4
0
( ) = , π π
6
≤ ≤
t
Finding the Displacement of
a Particle Given Acceleration
630–632 A particle moves according to the given
acceleration function over the given interval. First,
find the velocity function. Then find the displacement
of the particle. Remember: Displacement is the
change in position, velocity is the rate of change
in position with respect to time, and acceleration is
the rate of change in velocity with respect to time.
630. a(t) = t + 2, v
 
(0) = –6, 0 ≤ t ≤ 8
631. a(t) = 2t + 1, v
 
(0) = –12, 0 ≤ t ≤ 5
632. a(t) = sin t + cos t, v π
4
0
( ) = , π π
6
≤ ≤
t