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Questions and Answers
An object's position is described by $x(t) = 3 - 5t + 2t^2$, where $x$ is in meters and $t$ is in seconds. Determine the object's instantaneous velocity at $t = 3$ seconds.
An object's position is described by $x(t) = 3 - 5t + 2t^2$, where $x$ is in meters and $t$ is in seconds. Determine the object's instantaneous velocity at $t = 3$ seconds.
- 7 m/s (correct)
- -5 m/s
- 23 m/s
- 15 m/s
- 12 m/s
A vehicle accelerates uniformly from rest to a speed $v$ over a specific distance $d$. Assuming constant acceleration, what speed does the vehicle attain if it accelerates from rest over a distance of $3d$?
A vehicle accelerates uniformly from rest to a speed $v$ over a specific distance $d$. Assuming constant acceleration, what speed does the vehicle attain if it accelerates from rest over a distance of $3d$?
- $v\sqrt{3}$ (correct)
- $v/\sqrt{3}$
- $9v$
- $3v$
- $v/3$
Two objects' velocities are plotted on a graph of $v(t)$. The area under each curve is equivalent between $t = 0$ and $t = t_f$. Which quantity must be identical for both objects during this interval?
Two objects' velocities are plotted on a graph of $v(t)$. The area under each curve is equivalent between $t = 0$ and $t = t_f$. Which quantity must be identical for both objects during this interval?
- Total distance traveled
- Change in kinetic energy
- Final velocity
- Average acceleration
- Total displacement (correct)
Consider two objects starting at the same position, $x = 0$ at $t = 0$. Their velocities are represented by $v(t)$ curves, with the area under each curve being the same from $t = 0$ to $t = t_f$. If the velocity of object 1 is always greater than the velocity of object 2 in the interval $0 < t < t_f$, what can you conclude?
Consider two objects starting at the same position, $x = 0$ at $t = 0$. Their velocities are represented by $v(t)$ curves, with the area under each curve being the same from $t = 0$ to $t = t_f$. If the velocity of object 1 is always greater than the velocity of object 2 in the interval $0 < t < t_f$, what can you conclude?
The velocity of a particle is given by $v(t) = 5 + 6t^2$, where $v$ is in m/s and $t$ is in seconds. What is the average velocity of the particle between $t = 0$ and $t = 3$ seconds?
The velocity of a particle is given by $v(t) = 5 + 6t^2$, where $v$ is in m/s and $t$ is in seconds. What is the average velocity of the particle between $t = 0$ and $t = 3$ seconds?
An object starts from rest at $x = 0$ and moves with a constant acceleration of $a$. After $4$ seconds, its position is $x = 16$ m. What is the magnitude of its acceleration?
An object starts from rest at $x = 0$ and moves with a constant acceleration of $a$. After $4$ seconds, its position is $x = 16$ m. What is the magnitude of its acceleration?
An object is dropped from rest and experiences air resistance. Which of the following statements accurately describes how air resistance affects the object's acceleration as it falls?
An object is dropped from rest and experiences air resistance. Which of the following statements accurately describes how air resistance affects the object's acceleration as it falls?
Which of the following scenarios would result in a non-zero displacement?
Which of the following scenarios would result in a non-zero displacement?
An object oscillates around the origin. At time $t = 0$, it has a positive displacement and is moving toward the origin. Which of the following statements must be true?
An object oscillates around the origin. At time $t = 0$, it has a positive displacement and is moving toward the origin. Which of the following statements must be true?
What is the relationship between the area under an acceleration-time curve and the change in velocity?
What is the relationship between the area under an acceleration-time curve and the change in velocity?
Flashcards
Average Acceleration
Average Acceleration
The change in velocity divided by the change in time. In one dimension, it's the rate at which velocity changes.
Total Displacement
Total Displacement
The total change in position of an object, calculated by the area under the velocity-time curve.
Average Velocity
Average Velocity
The average rate of change of position over a given time interval.
Position Function
Position Function
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Velocity Function
Velocity Function
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One-Dimensional Kinematics
One-Dimensional Kinematics
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Study Notes
One-Dimensional Kinematics Practice Test Information
- This is AP Physics C: Mechanics Practice Test 11
- It contains 8 questions
- The time limit is 11 minutes
Question 1
- An object's position is given by x(t) = 2 + 4t - t², with x in meters and t in seconds.
- The average acceleration from t = 0 to t = 2 is -2 m/s².
Question 2
- A 400-kg car accelerates from rest to a final speed v over a distance d.
- With the same acceleration, the car can accelerate to √2v over a distance of 2d, starting from rest.
Question 3
- Two objects have the same area under their v(t) curves from t = 0 to t = tf.
- Both objects have the same total displacement from t = 0 to t = tf.
Question 4
- Two objects start at x = 0 at t = 0.
- Object 1 will initially be ahead, but it will lose its lead part way through the interval 0 < t < tf.
Question 5
- A particle's velocity is given by v(t) = 4 + 3t², with velocity in m/s and time in seconds.
- The average velocity in the interval t = 0 to t = 2 is 8 m/s.
Question 6
- An object starts at rest at x = 0 with constant acceleration.
- After 1 second, the object is at x = 2.
- The object's velocity at t = 2 s is 8 m/s.
Question 7
- An object falls from rest under gravity and air resistance, with a given velocity function.
- A specific position function is consistent with the velocity function.
Question 8
- There are five pairs of velocity and position functions.
- Three of the pairs are qualitatively consistent with each other.
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