To calculate the change in velocity when the mass changes and the acceleration remains constant, we can use Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Mathematically, Newton's second law can be written as:
Fnet = m * a
Where:
- Fnet is the net force acting on the object,
- m is the mass of the object, and
- a is the constant acceleration.
We can rearrange this equation to solve for the acceleration:
a = Fnet / m
Now, if the acceleration remains constant, we can assume that the net force acting on the object also remains constant. Therefore, we can rewrite the equation as:
Fnet = m1 * a = m2 * a
Where m1 and m2 represent the initial and final masses of the object, respectively.
Since the acceleration is constant, we can cancel it out from both sides of the equation:
m1 = m2
This equation indicates that the change in mass does not affect the change in velocity when the acceleration remains constant. The final velocity of an object undergoing constant acceleration depends only on the initial velocity and the time elapsed, not the mass of the object.
Therefore, when the acceleration remains constant, the change in velocity is independent of the change in mass.