The magnitude of kinetic energy of a body is k what is its kinetic energy if its velocity is doubled

This calculator will find the missing variable in the physics equation for Kinetic Energy of a rigid body, when two of the variables are known.

$$ KE = \dfrac{1}{2}mv^2 $$

Where:

KE = kinetic energy
m = mass of a body
v = velocity of a body

Kinetic Energy

Kinetic Energy is the energy an object has owing to its motion. In classical mechanics, kinetic energy (KE) is equal to half of an object's mass (1/2*m) multiplied by the velocity squared. For example, if a an object with a mass of 10 kg (m = 10 kg) is moving at a velocity of 5 meters per second (v = 5 m/s), the kinetic energy is equal to 125 Joules, or (1/2 * 10 kg) * 5 m/s2.

We use Joules, kilograms, and meters per second as our defaults, although any appropriate units for mass (grams, ounces, etc.) or velocity (miles per hour, millimeters per second, etc.) could certainly be used as well - the calculation is the same regardless.

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Answer

Verified

Hint: Velocity is defined as the rate of change of position of an object with respect to time. And the velocity is also defined as the amount of distance travelled by an object in a given amount of time. By using the velocity formula, the solution can be determined.

Complete step by step solution

1. Relation between velocity and kinetic energy$KE = \dfrac{1}{2} \times m{v^2}$Where, $KE$ is the kinetic energy, $m$ is the mass, $v$ is the velocity.$KE = \dfrac{1}{2} \times m{v^2}$If the velocity is doubled,$KE = \dfrac{1}{2} \times m{\left( {2v} \right)^2}$Squaring the terms inside the bracket,$KE = \dfrac{1}{2} \times m\left( {4{v^2}} \right)$By arranging the above equation,$KE = 4 \times \left( {\dfrac{1}{2} \times m{v^2}} \right)$By this equation, we clearly understand that the velocity is doubled then the kinetic energy becomes 4 times.2. Relation between velocity and accelerationAcceleration is the rate of change of velocity with respect to time. If the velocity is doubled, then it is due to acceleration only. In other words, by changing the acceleration, the velocity is doubled. So, if the velocity is doubled, the acceleration will not double.3. Relation between velocity and momentumBy Linear momentum equation,$p = m \times v$Where, $p$ is the momentum, $m$ is the mass, $v$ is the velocity.$p = m \times v$ As the velocity is doubled, $p = m \times \left( {2v} \right)$By arranging the above equation,$p = 2\left( {mv} \right)$From the above equation, it is clear that the velocity is doubled then the momentum also doubled. 4.Relation between velocity and potential energy:Actually, there is no relationship between velocity and potential energy. If the potential energy is changed to kinetic energy, then there is a relation between velocity and kinetic energy.

Hence, the option (C) is correct.

Note: The velocity of the object is doubled by changing the acceleration only. If the velocity is doubled its kinetic energy is multiplied by four times. And there is no relationship between the velocity and potential energy. So, if the velocity is doubled, momentum also doubles.