The Rate Race

Why it matters

Two robots carry identical bricks up identical stairs. One takes 15 seconds, one takes 5. Same work — so what exactly is the second one MORE of?

The idea in plain words

Work's stopwatch. Tap each term.

P = W ÷ t

A 40 kg girl climbs 25 steps of 16 cm each in 10 s (g = 10). Her power?

P = 160 W

• watt (W = J/s): P — power — how FAST energy is converted
• joule (J): W — work done or energy converted
• second (s): t — time taken
• h = 25 × 0.16 = 4 m
• W = mgh = 40 × 10 × 4 = 1600 J
• P = 1600 ÷ 10

Predict first

Robot B does the same 300 J of work in one-third the time. Its power is…

Power is the RATE of doing work: P = W/t. Shrink t, grow P — the work itself never changed.

• three times Robot A's — correct
• the same — same work is same power
• one-third of A's

What you do

Slide Robot B's time until its power bar reads exactly double Robot A's.

Check yourself

1 horse power (H.P.) is about…

1 H.P. ≈ 746 W — the old unit engines are still sold by.

A machine's power can also be written P = F × v because…

Push with force F at steady speed v and you deliver F·v watts — how car engines are rated.

Two pumps fill the same tank; pump A in 20 min, pump B in 60 min. Which does more WORK?

Same water lifted to the same height = same work. Speed only changes the power rating.

• 746 W — correct
• 100 W
• 1000 W
• P = W/t = F·S/t, and S/t is velocity — correct
• force equals velocity
• it can't — that formula is wrong
• Both do the same work — A just has more power — correct
• A does more work
• B does more work — it runs longer