Answer :
To determine which values best complete the chart, we need to understand the concept of constant acceleration.
When an object is moving with constant acceleration, its velocity increases uniformly over time. This means that the change in velocity per unit of time (i.e., the acceleration) remains constant.
Let's evaluate the provided options:
1. [tex]\( X: 0, Y: 0, Z: 1 \)[/tex]
2. [tex]\( X: 2, Y: 4, Z: 6 \)[/tex]
3. [tex]\( X: 3, Y: 3, Z: 3 \)[/tex]
4. [tex]\( X: 1, Y: 5, Z: 8 \)[/tex]
To find the correct option, we check each set for uniform increments in velocity:
1. For [tex]\( X: 0, Y: 0, Z: 1 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 0 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 0 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 1 \, m/s \)[/tex]
- The velocities do not increase uniformly, so this option is incorrect.
2. For [tex]\( X: 2, Y: 4, Z: 6 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 2 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 4 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 6 \, m/s \)[/tex]
- The velocities increase uniformly by [tex]\( 2 \, m/s \)[/tex] each second (constant acceleration); hence, this option is correct.
3. For [tex]\( X: 3, Y: 3, Z: 3 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- The velocities do not increase at all, so this option is incorrect.
4. For [tex]\( X: 1, Y: 5, Z: 8 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 1 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 5 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 8 \, m/s \)[/tex]
- The velocities do not increase uniformly (increments are not constant), so this option is incorrect.
Based on our analysis, the values that best complete the chart are:
[tex]\[ X: 2, Y: 4, Z: 6 \][/tex]
When an object is moving with constant acceleration, its velocity increases uniformly over time. This means that the change in velocity per unit of time (i.e., the acceleration) remains constant.
Let's evaluate the provided options:
1. [tex]\( X: 0, Y: 0, Z: 1 \)[/tex]
2. [tex]\( X: 2, Y: 4, Z: 6 \)[/tex]
3. [tex]\( X: 3, Y: 3, Z: 3 \)[/tex]
4. [tex]\( X: 1, Y: 5, Z: 8 \)[/tex]
To find the correct option, we check each set for uniform increments in velocity:
1. For [tex]\( X: 0, Y: 0, Z: 1 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 0 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 0 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 1 \, m/s \)[/tex]
- The velocities do not increase uniformly, so this option is incorrect.
2. For [tex]\( X: 2, Y: 4, Z: 6 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 2 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 4 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 6 \, m/s \)[/tex]
- The velocities increase uniformly by [tex]\( 2 \, m/s \)[/tex] each second (constant acceleration); hence, this option is correct.
3. For [tex]\( X: 3, Y: 3, Z: 3 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 3 \, m/s \)[/tex]
- The velocities do not increase at all, so this option is incorrect.
4. For [tex]\( X: 1, Y: 5, Z: 8 \)[/tex]:
- Velocity at [tex]\( t = 1 \, s \)[/tex] is [tex]\( 1 \, m/s \)[/tex]
- Velocity at [tex]\( t = 2 \, s \)[/tex] is [tex]\( 5 \, m/s \)[/tex]
- Velocity at [tex]\( t = 3 \, s \)[/tex] is [tex]\( 8 \, m/s \)[/tex]
- The velocities do not increase uniformly (increments are not constant), so this option is incorrect.
Based on our analysis, the values that best complete the chart are:
[tex]\[ X: 2, Y: 4, Z: 6 \][/tex]
