Question

prove that work done is equal to change in kinetic energy​

Answer 1

W = ΔKE

or

W = KEf− KEi

where,

• W is the work done against the resistance of inertia
• ΔKE is the change in kinetic energy (Δ is Greek letter capital delta)
• KEf is the final kinetic energy of the object (KEf = mvf2/2)
• KEi is the initial kinetic energy of the object (KEi = mvi2/2)

When you accelerate an object, you are doing work against inertia over the distance that the object is accelerated:

W = mad

where,

• W is the work in joules (J or kg-m²/s²)
• m is the mass of the object in kg
• a is the acceleration of the object in m/s²
• d is the distance the object moves in meters (m)

If the acceleration is constant, it is equal to the change in velocity over time:

a = (vf − vi)/t

Multiply both sides of the equation by t and divide by a:

t = (vf − vi)/a

Also, the distance traveled is the product of the average of the velocities and time:

d = t(vf + vi)/2

Substitute t = (vf − vi)/a in the equation:

d = (vf − vi)(vf + vi)/2a

Since (vf − vi)(vf + vi) = v2f − v2i, you get:

2ad = v2f − v2i

Multiply both sides of the equation by m and divide by 2:

mad = m(v2f − v2i)/2

mad = mv2f/2 − mv2i/2

W = KEf− KEi

∴ W = ΔKE

(∴ means "therefore")

__________________________________

Mark as brainlest ❤️

~ @ Sardonyx

Answer 2

Answer:

The work W done by the net force on a particle equals the change in the particle's kinetic energy KE: W=ΔKE=12mv2f−12mv2i W = Δ KE = 1 2 mv f 2 − 1 2 mv i 2 .