The Formula for Change in Kinetic Energy

Kinetic energy refers to the energy an object possesses due to its motion. It is defined as the work needed to accelerate the object from rest to its current velocity. The formula for kinetic energy is given by:

KE = 1/2 * m * v^2

Where:
- KE represents the kinetic energy of the object
- m is the mass of the object
- v is the velocity of the object

Understanding the Formula

The change in kinetic energy of an object can be calculated using the difference between the initial and final kinetic energy.

Change in Kinetic Energy (ΔKE) = KE_final - KE_initial

The formula for kinetic energy can be derived from the work-energy theorem. According to this theorem, the work done on an object is equal to the change in its kinetic energy.

Work (W) = ΔKE

The work done on an object can be expressed as the product of the force applied on it and the displacement it undergoes. In the case of kinetic energy, the work is done by the net force acting on the object. Thus, we can rewrite the equation as:

W = ΔKE = F * d

Using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

F = m * a

We can substitute this into the equation for work:

W = m * a * d

Since acceleration (a) is equal to the change in velocity (Δv) divided by the time taken (Δt):

a = Δv / Δt

We can replace acceleration in the work equation:

W = m * (Δv / Δt) * d

Rearranging the equation, we find:

W = m * Δv * (d / Δt)

Since velocity (v) is equal to displacement (d) divided by time (t):

v = d / t

We can substitute this into the equation:

W = m * Δv * v

Simplifying:

W = m * Δv * v = m * (Δv * v)

The term Δv * v represents the change in velocity (Δv) multiplied by the final velocity (v), which can be rewritten as v^2:

W = m * v^2

Finally, since work (W) is equal to the change in kinetic energy (ΔKE), we obtain the formula for kinetic energy:

KE = 1/2 * m * v^2

This formula allows us to calculate the change in kinetic energy of an object based on its mass and velocity.

It is so easy let me teach you step by stepfirst energy=force× displacementthen F= mass ×acceleration s= (v^2-u^2)/2afrom equation 1&2we get w=ma×(v^2-u^2)/2aw=1/2m(v^2-u^2)if initial velocity is 0then w=1/2mv^2