The kinetic energy of a body is the energy that is possessed due to its motion. Kinetic energy is the work needed to accelerate an object of a given mass from rest to its stated velocity. The derivation of kinetic energy is one of the most common questions asked in the examination. To excel in their examinations, students must properly understand the kinetic energy derivation method.
Kinetic energy depends upon the body’s velocity and mass. If the body’s velocity is zero, then the kinetic energy will also be zero. The derivation of kinetic energy is given below so that students can understand the concept more effectively. The kinetic energy formula derivation can be done using algebra and calculus. Both methods are explained below.
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Derivation of Kinetic Energy using Algebra
The kinetic energy derivation using only algebra is one of the best ways to understand the formula in-depth.
Starting with the work-energy theorem and then adding Newton’s second law of motion, we can say that,
Now, taking the kinematics equation and rearranging it, we get
Combining the 2 expressions, we get,
Now we already know that kinetic energy is the energy that it possessed due to its motion. So the kinetic energy at rest should be zero. Therefore, we can say that kinetic energy is:
Derivation of Kinetic Energy using Calculus
The derivation of kinetic energy using calculus is given below. To derive an expression for kinetic energy using calculus, we will not need to assume anything about the acceleration.
Starting with the work-energy theorem and Newton’s second law of motion we can say that
Now rearranging the differential terms to get the function and the integral into an agreement.
Now, we know that the kinetic energy of a body at rest is zero. So we can say that the kinetic energy is:
Read More: Newton’s Second Law of Motion
Frequently Asked Questions – FAQs
What is the definition of kinetic energy?
Can the kinetic energy be negative?
When is the kinetic energy maximum?
What happens to the kinetic energy when the speed decreases?
How is the kinetic energy different from the potential energy?
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