Energy and Motion II

Speed tells you how fast something is going.

$\text{speed} = \frac{\text{distance}}{\text{time}}$

Standard SI unit: metres per second (m/s). In everyday life we often use km/h. To convert km/h → m/s, divide by 3.6.

Worked example. A cyclist covers 12 km in 45 minutes. What is their average speed in m/s?

• 12 km = 12 000 m. 45 min = 45 × 60 = 2 700 s.
• Average speed = 12 000 / 2 700 = 4.44 m/s (or about 16 km/h).

A distance-time graph plots distance (y-axis) against time (x-axis). The line's behaviour tells you everything:

• Straight, sloping: constant speed.
• Horizontal: stationary.
• Curving up (getting steeper): speeding up.
• Curving down (flattening): slowing down.

The GRADIENT of a straight section gives the speed:

$\text{speed} = \frac{\Delta\text{distance}}{\Delta\text{time}}$

For a curve, you can find the speed at any one moment by drawing a tangent and measuring its gradient — but you only need this for stretch tasks in MYP Year 3-4.

Energy is always conserved — but not all of it ends up doing the JOB you want. Efficiency measures the fraction that does:

$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%$

Some examples:

• LED lamp: ~90% efficient (most input energy becomes light).
• Incandescent bulb: ~5% efficient (most becomes heat).
• Petrol car: ~25% (most fuel energy lost as heat in the engine and exhaust).
• Electric motor: 80-95% (most input becomes mechanical work).
• Human body (working hard): ~25% (rest becomes body heat).

The wasted energy isn't gone — it just ends up in less useful stores. A Sankey diagram shows this beautifully: arrow width = amount of energy.

Worked example. A motor takes in 200 J of electrical energy and produces 160 J of kinetic energy. Find the efficiency.

Efficiency = 160 / 200 × 100 = 80%. The other 40 J becomes thermal energy in the wires, bearings and surroundings.