85
Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem
Finding the Distance Traveled
by a Particle Given the
Velocity
625–629 A particle moves according to the given
velocity function over the given interval. Find the
total distance traveled by the particle. Remember:
Velocity is the rate of change in position with respect
to time.
625. v(t) = 2t – 4, 0 ≤ t ≤ 5
626. v(t) = t
2
– t – 6, 2 ≤ t ≤ 4
627. v(t) = 2 cos t, 0 ≤ t ≤ π
628. v(t) = sin t – cos t, − ≤ ≤
π
π
6
2
t
629. v t
t
( ) =
−4, 1 ≤ t ≤ 25
619. Water is flowing into a pool at a rate of w'(t),
where t is measured in minutes and w'(t) is
measured in gallons per minute. What does
′
∫ w t dt
( )
60
120
represent?
Finding the Displacement of a
Particle Given the Velocity
620–624 A particle moves according to the given
velocity function over the given interval. Find
the displacement of the particle. Remember:
Displacement is the change in position, and velocity
is the rate of change in position with respect to time.
620. v(t) = 2t – 4, 0 ≤ t ≤ 5
621. v(t) = t
2
– t – 6, 2 ≤ t ≤ 4
622. v(t) = 2 cos t, 0 ≤ t ≤ π
623. v(t) = sin t – cos t, − ≤ ≤
π
π
6
2
t
624. v t
t
( ) =
−4, 1 ≤ t ≤ 25