It becomes half.
Explanation
Kinetic energy (KE) is the energy possessed by an object by virtue of its motion. It is mathematically expressed as half the product of the object's mass ($m$) and the square of its velocity ($v$). The standard formula is:
$KE = \frac{1}{2}mv^2$
Mathematical Analysis:
Let the initial kinetic energy be denoted as $KE_1$.
- Initial Mass = $m$
- Initial Velocity = $v$
- $KE_1 = \frac{1}{2}mv^2$
According to the problem, the mass is doubled and the velocity is halved. Let the new kinetic energy be $KE_2$.
- New Mass ($m'$) = $2m$
- New Velocity ($v'$) = $\frac{v}{2}$
Substituting these new values into the formula:
$KE_2 = \frac{1}{2}(2m)\left(\frac{v}{2}\right)^2$
$KE_2 = \frac{1}{2}(2m)\left(\frac{v^2}{4}\right)$
$KE_2 = \frac{1}{2} \left( \frac{1}{2}mv^2 \right)$
$KE_2 = \frac{1}{2} KE_1$
Therefore, the new kinetic energy is half of the original value.
Key Takeaway:
Kinetic energy is directly proportional to mass and directly proportional to the square of velocity. Consequently, changes in velocity have a quadratic effect on energy, whereas changes in mass have a linear effect.