Kinetic energy

Kinetic energy is the energy something has because it is moving: a cycling bicycle, a rolling ball.

Where does the formula come from? A steady force F pushes a mass m over a distance s, and its speed goes from u to v. Two things you already know:

• From Chapter 4: v² = u² + 2as, so s = (v² – u²) ÷ 2a.
• From Chapter 6: F = ma.

Multiply them: W = F × s = ma × (v² – u²)/2a. The a cancels, leaving W = ½m(v² – u²). The work done equals the change in ½mv².

If the object starts from rest (u = 0), all that work becomes its kinetic energy:

K = ½mv².

It is measured in joules and has no direction.

How work changes it:

• Positive work: speed and kinetic energy go up.
• Negative work: they go down.
• No work: kinetic energy stays the same, wherever the object is.

Speed matters most. Because speed is squared, doubling the speed makes the kinetic energy four times as big: ½m(2v)² = 4 × ½mv². This is the same reason the braking distance was four times longer in Chapter 4.

A fast bowler's ball: 0.2 kg at 154.8 km h⁻¹ (43 m s⁻¹). K = ½ × 0.2 × 43² = 184.9 J.

A fighter jet landing on a ship's deck: a 15000 kg jet is stopped by a force of 367500 N over 100 m. The work done by the force equals its kinetic energy: ½ × 15000 × v² = 367500 × 100, so it was landing at v = 70 m s⁻¹.