Name_______________________
Period_____
Calculus
Lesson 7.1 Integral as Net Change
The function v (t ) is the velocity in m/sec of a particle moving along the x-axis. Use analytic methods to do
each of the following:
(a) Determine when the particle is moving to the right, to the left and stopped.
(b) Find the particle’s displacement for the given time interval. If s(0)  3 , what is the particle’s final position?
(c) Find the total distance traveled by the particle.
1. v(t )  6sin 3t , 0  t   / 2
2. v(t )  4  t , 0  t  4
3. The particle starts at x = 2 when t = 0.
(a) Find where the particle is at the end of the trip.
(b) Find the total distance traveled by the particle.
4. A developing country consumes oil at a rate given by r (t )  20e0.2t million barrels per year, where t is time
measured in years, for 0  t  10 . Which of the following expressions gives the amount of oil consumed by the
country during the time interval 0  t  10 ?
10
(a) r (10)
(b) r (10)  r (0)
(c)  r   t  dt
0
10
(d)
 r  t  dt
0
(e) 10  r 10 
1992 AB 2
A particle moves along the x-axis so that its velocity at time t, 0  t  5 , is given by v(t )  3(t  1)(t  3) . At time
t = 2, the position of the particle is x(2)  0 .
(a) Find the minimum acceleration of the particle.
(b) Find the total distance traveled by the particle.
(c) Find the average velocity of the particle of the interval 0  t  5 .
1997 AB 1
A particle moves along the x-axis with velocity given by v(t )  3t 2  2t  1 for any time t  0 . The position x(t )
is 5 for t =2.
(a) Write a polynomial expression for the position of the particle at any time t  0 .
(b) For what values of t, 0  t  3 is the instantaneous velocity of the particle the same as the average velocity
of the particle on the closed interval [0,3]?
(c) Find the total distance traveled by the particle from time t = 0 until t = 3.
AP Practice AB 2010 Form B