If the mass of an object is doubled, how does this affect its kinetic energy at the same velocity?

Kinetic energy is defined by the equation ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the object and ( v ) is its velocity. When the mass of an object is doubled while maintaining the same velocity, you can substitute ( 2m ) for ( m ) in the equation.

The new kinetic energy would be ( KE_{\text{new}} = \frac{1}{2} (2m)v^2 = 2 \left( \frac{1}{2} mv^2 \right) ). This shows that the kinetic energy of the object becomes twice its original value, as the factor of mass directly scales the kinetic energy.

This relationship highlights how kinetic energy is directly proportional to mass when speed is held constant. Thus, doubling the mass results in the kinetic energy being doubled, supporting the idea that mass has a linear influence on kinetic energy in this scenario.