Question

if the velocity of an airplane is doubled, then its kinetic energy will increase by a factor of
a 2
b it will remain the same
c 8
d 4

Explanation:

Step1: Write the formula for kinetic energy

The formula for kinetic energy is \(K = \frac{1}{2}mv^{2}\), where \(m\) is the mass of the object and \(v\) is its velocity.

Step2: Find the new kinetic energy when velocity is doubled

Let the initial velocity be \(v\), so the initial kinetic energy \(K_{1}=\frac{1}{2}mv^{2}\). When the velocity is doubled (\(v_{2} = 2v\)), the new kinetic energy \(K_{2}=\frac{1}{2}m(2v)^{2}\).
Expand \((2v)^{2}\): \(K_{2}=\frac{1}{2}m\times4v^{2}=4\times\frac{1}{2}mv^{2}\).
Since \(K_{1}=\frac{1}{2}mv^{2}\), we can see that \(K_{2} = 4K_{1}\).

Answer:

d. 4