If the mass of a moving object is doubled and its velocity is halved, how is its kinetic energy affected?

The correct option is

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.