When the mass and speed of an object are doubled, the kinetic energy of the object ____________. becomes double becomes four times higher becomes eight times higher remains…
When the mass and speed of an object are doubled, the kinetic energy of the object ____________. becomes double becomes four times higher becomes eight times higher remains unchanged
The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the object and \( v \) is its speed.
If both the mass and speed of the object are doubled, we can express the new kinetic energy as follows:
Let the original mass be \( m \) and the original speed be \( v \). The original kinetic energy is:
\[ KE_{\text{original}} = \frac{1}{2}mv^2 \]
Now, if both mass and speed are doubled, the new mass is \( 2m \) and the new speed is \( 2v \). The new kinetic energy is:
\[ KE_{\text{new}} = \frac{1}{2}(2m)(2v)^2 \] \[ KE_{\text{new}} = \frac{1}{2}(2m)(4v^2) \] \[ KE_{\text{new}} = 4 \cdot \frac{1}{2}mv^2 \] \[ KE_{\text{new}} = 4 \cdot KE_{\text{original}} \]
Thus, when the mass and speed of an object are doubled, the kinetic energy of the object becomes four times higher.
So the answer is: becomes four times higher.
