derive the expression for kinetic energy and work, energy theorm?
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KINETIC ENERGY
Derivation using algebra alone (and assuming acceleration is constant). Start from the work-energy theorem, then add in Newton's second law of motion.
ΔK = W = FΔs = maΔs
Take the the appropriate equation from kinematics and rearrange it a bit.
v2 = v02 + 2aΔs aΔs = v2 − v022
Combine the two expressions.
ΔK = m ⎛
⎝v2 − v02⎞
⎠2
And now something a bit unusual. Expand.
ΔK = 1 mv2 − 1 mv0222
If kinetic energy is the energy of motion then, naturally, the kinetic energy of an object at rest should be zero. Therefore, we don't need the second term
K=1/2mv2
Derivation using algebra alone (and assuming acceleration is constant). Start from the work-energy theorem, then add in Newton's second law of motion.
ΔK = W = FΔs = maΔs
Take the the appropriate equation from kinematics and rearrange it a bit.
v2 = v02 + 2aΔs aΔs = v2 − v022
Combine the two expressions.
ΔK = m ⎛
⎝v2 − v02⎞
⎠2
And now something a bit unusual. Expand.
ΔK = 1 mv2 − 1 mv0222
If kinetic energy is the energy of motion then, naturally, the kinetic energy of an object at rest should be zero. Therefore, we don't need the second term
K=1/2mv2
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