An object’s speed is increased by a factor of three. How does the object’s momentum change?
The Correct Answer and Explanation is:
When the speed of an object is increased by a factor of three, its momentum will increase by a factor of three. To understand this, we need to look at the relationship between momentum and velocity.
Momentum (ppp) is given by the equation:p=m⋅vp = m \cdot vp=m⋅v
where:
- ppp is the momentum,
- mmm is the mass of the object,
- vvv is the velocity (or speed) of the object.
When the speed increases, assuming the mass of the object stays the same, the momentum will be directly proportional to the speed. That means if the speed increases by a factor of three, the momentum will also increase by a factor of three. This can be seen mathematically:
Let the initial speed of the object be vvv. The initial momentum is:pinitial=m⋅vp_{\text{initial}} = m \cdot vpinitial=m⋅v
Now, if the speed increases by a factor of three, the new speed becomes 3v3v3v. The new momentum is:pnew=m⋅(3v)=3⋅(m⋅v)=3⋅pinitialp_{\text{new}} = m \cdot (3v) = 3 \cdot (m \cdot v) = 3 \cdot p_{\text{initial}}pnew=m⋅(3v)=3⋅(m⋅v)=3⋅pinitial
Thus, the momentum increases by a factor of three.
This is a simple, linear relationship between speed and momentum because momentum is directly proportional to velocity. So, any change in the speed of an object will result in a proportional change in its momentum, assuming the mass remains constant. Therefore, when the speed is increased by a factor of three, the momentum also increases by a factor of three.
