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How is your kinetic energy related to your speed?

Kinetic Energy is proportional to the square of the velocity. If the velocity is doubled, the KE is 4 times as much.

I don't remember ever seeing the KE formula derived. I derived it from motion and work equations.

1) Work input = Force * distance

Work input causes increase in KE

Force * distance = increase in KE

If the object is at rest initially,

2) Work input = Force * distance = KE

3) Force * distance = KE

Force = mass * acceleration

4) F = m*a

Acceleration = (Vf - Vi) ÷ time, Vi = 0,Vf = V

5) a = V ÷ t

Substituting V ÷ t for a

6) F = m*( V ÷ t)

Distance = Average velocity * time

7) Average velocity = (Vi + Vf) ÷ 2, Vi = initial velocity, Vf =final velocity

If the object is at rest initially, Vi = 0, Vf is the velocity at specific time.

8) Average velocity = V ÷ 2

9) Distance = (V ÷ 2) * time

10)Force * distance = KE

……………….From Eq.#6………..From Eq#9

11) F = m*( V ÷ t)…… Distance = (V ÷ 2) * t

12)Force * distance = m*( V ÷ t) * (V ÷ 2) * t

Be careful of numerators and denominators. What is divided by what!

13)Force * distance = (M * V^2) Substituting from Eq #2 reversed, Work input = Force * distance

14)Work input = (M * V^2) ÷ 2

15) Kinetic Energy = ½ * Mass velocity^2

16)Work input = ½ * Mass velocity^2

There it is, the Kinetic energy formula derived from work and motion equations.

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15y ago

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