When the mass and speed of an object are doubled, the kinetic energy of the object ____________.

The kinetic energy (KE) of an object is given by the formula:

\[ KE = \frac{1}{2} m v^2 \]

where \( m \) is the mass of the object and \( v \) is its speed.

If both the mass \( m \) and the speed \( v \) of an object are doubled, we can see how the kinetic energy changes:

• New mass \( m' = 2m \)
• New speed \( v' = 2v \)

Now, substituting into the kinetic energy formula, we have:

\[ KE' = \frac{1}{2} (2m) (2v)^2 \] \[ KE' = \frac{1}{2} (2m) (4v^2) \] \[ KE' = 4mv^2 \]

Since the original kinetic energy \( KE = \frac{1}{2} mv^2 \), we can relate the new kinetic energy to the original:

\[ KE' = 4 \left(\frac{1}{2} mv^2\right) = 4 KE \]

Thus, when the mass and speed of an object are both doubled, the kinetic energy of the object increases by a factor of 4.