- Information
- AI Chat
1+Motion+Practice+ Blank
Assignment for Motion
Course
Calculus 1 (MTH 263)
82 Documents
Students shared 82 documents in this course
University
Northern Virginia Community College
Academic year: 2024/2025
Uploaded by:
0followers
3Uploads
0upvotes
Preview text
Motion Practice
Non-Calculator Multiple Choice
- A particle moves along the 𝑥𝑥-axis so that at time 𝑡𝑡 ≥ 0 its position is given by 𝑥𝑥(𝑡𝑡) = 2𝑡𝑡 3 − 21 𝑡𝑡 2 + 72𝑡𝑡 − 53. At what time 𝑡𝑡 is the particle at rest?
(A) 𝑡𝑡 = 1 only (B) 𝑡𝑡 = 3 only (C) 𝑡𝑡 = 7 2 only (D) 𝑡𝑡 = 3 and 𝑡𝑡 =
7 2 (E) 𝑡𝑡 = 3 and 𝑡𝑡 = 4
- For 𝑡𝑡 ≥ 0 , the velocity of a particle moving along the 𝑥𝑥-axis is given by 𝑣𝑣(𝑡𝑡) = (𝑡𝑡 − 5)(𝑡𝑡 − 2) 2. At what values of 𝑡𝑡 is the acceleration of the particle equal to 0?
(A) 2 only (B) 4 only (C) 2 and 4 (D) 2 and 5
- A particle moves along a straight line. The graph of the particle’s position 𝑥𝑥(𝑡𝑡) at time 𝑡𝑡 is shown above for 0 < 𝑡𝑡 < 6. The graph has horizontal tangents at 𝑡𝑡 = 1 and 𝑡𝑡 = 5 and a point of inflection at 𝑡𝑡 = 2. For what values of 𝑡𝑡 is the velocity of the particle increasing?
(A) 0 < 𝑡𝑡 < 2 (B) 1 < 𝑡𝑡 < 5 (C) 2 < 𝑡𝑡 < 6 (D) 3 < 𝑡𝑡 < 5 only (E) 1 < 𝑡𝑡 < 2 and 5 < 𝑡𝑡 < 6
- A particle moves along the 𝑥𝑥-axis with velocity given by 𝑣𝑣(𝑡𝑡) = 3𝑡𝑡 2 + 6𝑡𝑡 for time 𝑡𝑡 ≥ 0. If the particle is at position 𝑥𝑥 = 2 at time 𝑡𝑡 = 0, what is the position of the particle at time 𝑡𝑡 = 1?
(A) 4 (B) 6 (C) 0 (D) 11 (E) 12
- The velocity of a particle moving on a line at time 𝑡𝑡 is 𝑣𝑣(𝑡𝑡) = 3𝑡𝑡 1 / 2 + 5𝑡𝑡 3 / 2 meters per second. How many meters did the particle travel from 𝑡𝑡 = 0 to 𝑡𝑡 = 4?
(A) 32 (B) 40 (C) 64 (D) 80 (E) 184
- If the position of a particle on the 𝑥𝑥-axis at the time 𝑡𝑡 is − 5 𝑡𝑡 2 , then the average velocity of the particle for 0 ≤ 𝑡𝑡 ≤ 3 is
(A) -45 (B) -30 (C) -15 (D) -10 (E) -
- A particle travels is straight line with a constant acceleration of 3 meters per second. If the velocity of the particle is 10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity increases from 4 meters per second to 10 meters per second?
(A) 20 m (B) 14 m (C) 7 m (D) 6 m (E) 3 m
- A particle moves along the 𝑥𝑥-axis. The velocity of the particle at time 𝑡𝑡 is 6 𝑡𝑡 − 𝑡𝑡 2. What is the total distance traveled by the particle from 𝑡𝑡 = 0 to 𝑡𝑡 = 3?
(A) 3 (B) 6 (C) 9 (D) 18 (E) 27
AP Calc AB: AP Exam Review Name__________________
Date_____________ Pd___
Was this document helpful?
1+Motion+Practice+ Blank
Course: Calculus 1 (MTH 263)
82 Documents
Students shared 82 documents in this course
University: Northern Virginia Community College
Was this document helpful?
Motion Practice
Non-Calculator Multiple Choice
1. A particle moves along the 𝑥𝑥-axis so that at time 𝑡𝑡 ≥ 0 its position is given by 𝑥𝑥(𝑡𝑡)= 2𝑡𝑡3−21𝑡𝑡2+72𝑡𝑡 − 53. At what
time 𝑡𝑡 is the particle at rest?
(A) 𝑡𝑡= 1 only (B) 𝑡𝑡= 3 only (C)
𝑡𝑡=7
2 only (D) 𝑡𝑡= 3 and 𝑡𝑡=7
2 (E) 𝑡𝑡= 3 and 𝑡𝑡= 4
2. For 𝑡𝑡 ≥ 0, the velocity of a particle moving along the 𝑥𝑥-axis is given by 𝑣𝑣(𝑡𝑡)= (𝑡𝑡 − 5)(𝑡𝑡 − 2)2. At what values of 𝑡𝑡 is
the acceleration of the particle equal to 0?
(A) 2 only (B) 4 only (C) 2 and 4 (D) 2 and 5
3. A particle moves along a straight line. The graph of the particle’s position 𝑥𝑥(𝑡𝑡) at time 𝑡𝑡 is
shown above for 0 < 𝑡𝑡< 6. The graph has horizontal tangents at 𝑡𝑡= 1 and 𝑡𝑡= 5 and a point of
inflection at 𝑡𝑡= 2. For what values of 𝑡𝑡 is the velocity of the particle increasing?
(A) 0 < 𝑡𝑡< 2 (B) 1<𝑡𝑡< 5 (C) 2 < 𝑡𝑡< 6 (D)
3 < 𝑡𝑡< 5 only (E) 1 < 𝑡𝑡< 2 and 5 < 𝑡𝑡< 6
4. A particle moves along the 𝑥𝑥-axis with velocity given by 𝑣𝑣(𝑡𝑡)= 3𝑡𝑡2+ 6𝑡𝑡 for time 𝑡𝑡 ≥ 0. If the particle is at position
𝑥𝑥= 2 at time 𝑡𝑡= 0, what is the position of the particle at time 𝑡𝑡= 1?
(A) 4 (B) 6 (C) 0 (D) 11 (E) 12
5. The velocity of a particle moving on a line at time 𝑡𝑡 is 𝑣𝑣(𝑡𝑡)= 3𝑡𝑡1/2+ 5𝑡𝑡3/2 meters per second. How many meters did
the particle travel from 𝑡𝑡= 0 to 𝑡𝑡= 4?
(A) 32 (B) 40 (C) 64 (D) 80 (E) 184
6. If the position of a particle on the 𝑥𝑥-axis at the time 𝑡𝑡 is −5𝑡𝑡2, then the average velocity of the particle for 0≤ 𝑡𝑡 ≤ 3 is
(A) -45 (B) -30 (C) -15 (D) -10 (E) -5
7. A particle travels is straight line with a constant acceleration of 3 meters per second. If the velocity of the particle is
10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity
increases from 4 meters per second to 10 meters per second?
(A) 20 m (B) 14 m (C) 7 m (D) 6 m (E) 3 m
8. A particle moves along the 𝑥𝑥-axis. The velocity of the particle at time 𝑡𝑡 is 6𝑡𝑡 − 𝑡𝑡2. What is the total distance traveled
by the particle from
𝑡𝑡= 0 to 𝑡𝑡= 3?
(A) 3 (B) 6 (C) 9 (D) 18 (E) 27
AP Calc AB: AP Exam Review
Name__________________
Date_____________ Pd___
