AP Calculus AB Accumulated Change II



AP Calculus AB

Total Distance and Net Change Worksheet

In problems 1-4, v is the velocity in meters per second of a body moving along a line. (a) Graph v to find where it is positive and where it is negative. Then find (b) the total distance traveled by the body during the given time interval and (c) the net change in the body's position.

1. v = [pic] , [pic]

2. v = 49 - 9.8 t , [pic]

3. v = 6 ( t -1) (t -2), [pic]

4. v = 4 cos 2t, [pic]

5. In this problem, a is the acceleration in meters per second per second (m/sec2) of a body moving along a line from t = 0 to time t = 2. The body's velocity at t = 0 is v (0). Find the net change in the body's position over the time interval. (Hint: First find a formula for v (t ).)

a = -4(2 cos 2( t , v (0) = 2

6. Below are the velocity graphs of four bodies moving along straight lines for various intervals of time. Find the total distance traveled by each body and the net change of the body's position.

7. The table below shows the speed of an automobile every 10 seconds form start to stop on a 2-minute trip. Use the Trapezoidal Rule to estimate how far the car went. (Note that 2 minutes is 1/30 of an hour)

|Selected Speeds of a Car on a 2-minute Trip |

|Time (s) |Speed (mph) |Time (s) |Speed (mph) |

|0 |0 |70 |66 |

|10 |32 |80 |66 |

|20 |51 |90 |58 |

|30 |57 |100 |40 |

|40 |54 |110 |6 |

|50 |64 |120 |0 |

|60 |66 | | |

ANSWERS: TD = Total Distance

NC = Net change in position

1. TD = 20

NC = 0

2. TD = 245

NC = 0

3. TD = 6

NC = 4

4. TD = 8

NC = 0

5. NC = 4 6. a. TD = 2 NC = 2 7. [pic] miles

b. TD = 4 NC = 0

c. TD = 4 NC = 4

d. TD = 2 NC = 2

-----------------------

1

1

0

[pic]

2

0

0

1

4

4

3

5

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download