What does doubling the mass of an object while keeping energy constant lead to regarding travel distance?

When the mass of an object is doubled while keeping the energy constant, the travel distance is affected due to the relationship between kinetic energy, mass, and velocity. Kinetic energy (KE) is calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity.

If the mass is doubled, we then have KE = 1/2 (2m)v² = mv². Since the total energy remains constant, we can set this equal to the original kinetic energy. Therefore, we can rearrange the formulas:

1/2 mv₁² = 1/2 (2m)v₂².

This implies that the initial kinetic energy (when the object had mass m) is equal to the final kinetic energy (when the object has mass 2m). Solving for the new velocity (v₂) reveals that the velocity decreases because it is now divided by the square root of 2 in order to compensate for the increased mass while the energy remains unchanged. This drop in velocity leads to a corresponding decrease in travel distance, as distance is directly related to speed when time is constant.

In summary, maintaining constant energy while doubling the mass results in a lower velocity, which