An object’s speed is increased by a factor of three.
How does the object’s momentum change?
MultipleChoice :
1) It decreases by a factor of three.
2) It increases by a factor of more than three.
3) The momentum does not change.
4) It increases by a factor of three.
5) It decreases by a factor of more than three.
6) There is not enough information.
The correct answer and explanation is :
The correct answer is:
4) It increases by a factor of three.
Explanation:
Momentum is the product of an object’s mass and velocity. Mathematically, this is represented as:
[
p = mv
]
Where:
- ( p ) is the momentum of the object,
- ( m ) is the mass of the object, and
- ( v ) is the velocity (speed in this context).
When the object’s speed is increased by a factor of three, its velocity is tripled. Since mass does not change, the momentum will be directly affected by the change in speed. The relationship between momentum and speed is linear, meaning that if the speed increases by a factor of three, the momentum also increases by a factor of three.
Here’s how it works:
- Before the speed increase, the momentum is ( p = m \times v ), where ( v ) is the initial speed.
- After the speed increase, the new speed is ( 3v ), so the new momentum becomes:
[
p’ = m \times 3v = 3(m \times v) = 3p
]
Therefore, the momentum becomes three times larger than it was originally.
Why the other options are incorrect:
1) “It decreases by a factor of three.”: This is not correct because increasing the speed increases the momentum, not decreases it.
2) “It increases by a factor of more than three.”: This is incorrect because momentum increases linearly with velocity. If the speed increases by a factor of three, the momentum also increases by exactly a factor of three, not more.
3) “The momentum does not change.”: This is wrong because the momentum is directly proportional to the velocity. If the speed changes, the momentum changes.
5) “It decreases by a factor of more than three.”: Again, this is incorrect for the same reason as option 1—momentum increases with speed, not decreases.
6) “There is not enough information.”: This is incorrect because the relationship between momentum and speed is well-known and can be deduced with the given information (i.e., that the speed increases by a factor of three).
In summary, when the object’s speed is increased by a factor of three, its momentum increases by exactly three times, making option 4 the correct choice.