Key Idea: The amount of kinetic energy (motion energy) an object has is proportional to the mass of the object and increases rapidly with increasing speed.
Students should know that:
- For an object traveling at constant speed, the kinetic energy of the object is directly proportional to the mass of the object. For example, doubling the object’s mass will double the amount of kinetic energy the object has (assuming constant speed) and halving the object’s mass will halve the amount of kinetic energy the object has (assuming constant speed).
- For an object of constant mass, the kinetic energy is directly proportional to the square of the speed. For example, doubling the object’s speed will increase the amount of kinetic energy the object has by four times (assuming constant mass) and halving the object’s speed will decrease the amount of kinetic energy the object has by a factor of four (assuming constant mass).
- The relationships between an object’s speed, mass, and kinetic energy are mathematically represented by the equation KE = ½mv2, where v is the speed and m is the mass of the object.
Boundaries:
- This idea refers to motion with respect to the surface of the earth. An object is considered to be “not moving” if its position with respect to a point on the surface of the earth is not changing.
- Items may show objects moving in a straight line, vibrating back and forth, or rotating. In all cases, students are expected to know only that the amount of energy of motion the object has depends on its speed and its mass. In items, comparisons will be made between objects moving in the same manner (i.e., both rotating) and with the same distribution of mass from the origin.
- In cases dealing with rotational motion, students are not expected to be familiar with the concepts of angular velocity and moment of inertia or the units of angular velocity and moment of inertia. They are expected to know that if the speed at which an object is rotating increases, the kinetic energy increases. In these items, the distribution of mass from the origin will remain constant and the speed of rotation will only be qualitatively described (increasing or decreasing).
| Item ID Number |
Knowledge Being Assessed | Grades 4–5 |
Grades 6–8 |
Grades 9–12 |
Select This Item for My Item Bank |
|---|---|---|---|---|---|
N/A | 33% |
39% |
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||
N/A | 34% |
37% |
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||
N/A | 33% |
37% |
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||
N/A | 29% |
28% |
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Kinetic energy is proportional to the speed squared. (Item uses line graphs.) | N/A | 21% |
34% |
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|
N/A | 19% |
22% |
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N/A | 15% |
23% |
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||
N/A | 9% |
14% |
|
Misconception |
Student Misconception |
Grades 4–5 |
Grades |
Grades |
|---|---|---|---|---|
N/A | 32% |
34% | ||
N/A | 35% |
27% | ||
N/A | 37% |
23% | ||
N/A | 24% |
26% | ||
N/A | 23% |
21% | ||
N/A | 21% |
18% | ||
N/A | 17% |
15% |
Frequency of selecting a misconception was calculated by dividing the total number of times a misconception was chosen by the number of times it could have been chosen, averaged over the number of students answering the questions within this particular idea.