The particle starts from rest at t = 0. What is the magnitude p of the momentum of the particle at time t? Assume that t > 0. The particle starts from rest at t = 0. What is the magnitude v of the velocity of the particle at time t? Assume that t > 0. The particle has momentum of magnitude p1 at a certain instant. What is p2, the magnitude of its momentum Δt seconds later?

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  • The particle starts from rest at t = 0. What is the magnitude p of the momentum of the particle at time t? Assume that t > 0.
  • The particle starts from rest at t = 0. What is the magnitude v of the velocity of the particle at time t? Assume that t > 0.
  • The particle has momentum of magnitude p1 at a certain instant. What is p2, the magnitude of its momentum Δt seconds later?

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Here \( F \), \( v_1 \), and \( v_2 \) are the *components* of the corresponding vector quantities along the chosen coordinate axis. If the motion in question is two-dimensional, it is often useful to apply equation (3) to the \( x \) and \( y \) components of motion separately.
Transcribed Image Text:Here \( F \), \( v_1 \), and \( v_2 \) are the *components* of the corresponding vector quantities along the chosen coordinate axis. If the motion in question is two-dimensional, it is often useful to apply equation (3) to the \( x \) and \( y \) components of motion separately.
The image is a diagram representing vectors situated around the origin of an x-y coordinate plane. There are eight vectors, each labeled with a number (1 through 8), illustrating different directions.

- **x-axis**: The horizontal line. Vectors labeled 3 and 7 align with this axis. Vector 3 is directed rightward (positive x-direction), while vector 7 is leftward (negative x-direction).
- **y-axis**: The vertical line. Vectors labeled 1 and 5 align with this axis. Vector 1 points upward (positive y-direction), and vector 5 points downward (negative y-direction).

The vectors are as follows:

1. Vector 1 points upwards toward the positive y-direction.
2. Vector 2 points at an angle, midway between the positive x and y axes.
3. Vector 3 points directly along the positive x-direction.
4. Vector 4 points at an angle, midway between the positive x-axis and negative y-axis.
5. Vector 5 points directly downward along the negative y-direction.
6. Vector 6 points at an angle, midway between the negative x and y axes.
7. Vector 7 points directly along the negative x-direction.
8. Vector 8 points at an angle, midway between the negative x-axis and positive y-axis.

The vectors radiate symmetrically from the origin, demonstrating different angular directions within the coordinate plane.
Transcribed Image Text:The image is a diagram representing vectors situated around the origin of an x-y coordinate plane. There are eight vectors, each labeled with a number (1 through 8), illustrating different directions. - **x-axis**: The horizontal line. Vectors labeled 3 and 7 align with this axis. Vector 3 is directed rightward (positive x-direction), while vector 7 is leftward (negative x-direction). - **y-axis**: The vertical line. Vectors labeled 1 and 5 align with this axis. Vector 1 points upward (positive y-direction), and vector 5 points downward (negative y-direction). The vectors are as follows: 1. Vector 1 points upwards toward the positive y-direction. 2. Vector 2 points at an angle, midway between the positive x and y axes. 3. Vector 3 points directly along the positive x-direction. 4. Vector 4 points at an angle, midway between the positive x-axis and negative y-axis. 5. Vector 5 points directly downward along the negative y-direction. 6. Vector 6 points at an angle, midway between the negative x and y axes. 7. Vector 7 points directly along the negative x-direction. 8. Vector 8 points at an angle, midway between the negative x-axis and positive y-axis. The vectors radiate symmetrically from the origin, demonstrating different angular directions within the coordinate plane.
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