Power = Work / Time

Power measures how fast work is being done — it's the rate of energy transfer. Two motors can do the same total work, but the more powerful one does it in less time.

The Formula

$P = \dfrac{W}{t} = \dfrac{\text{work done}}{\text{time taken}}$

Units: 1 watt = 1 joule per second. Other common units: 1 horsepower ≈ 745.7 watts.

Step-by-Step Solution

Given: $m = 100\;\text{kg}$ lifted by $h = 10\;\text{m}$ in $t = 5\;\text{s}$, $g = 9.81\;\text{m/s}^{2}$.

Find: The average power $P$.

---

Step 1 — Compute the work done.

Lifting the mass by $h$ at constant speed (or with no net acceleration at the end) requires work equal to the gain in gravitational potential energy:

$W = mgh = (100)(9.81)(10) = 9810\;\text{J}$

Step 2 — Divide by time.

$P = \dfrac{W}{t} = \dfrac{9810}{5} = 1962\;\text{W}$

Step 3 — Convert to horsepower for intuition.

$P = \dfrac{1962}{745.7} \approx 2.63\;\text{hp}$

So the motor outputs about 2.6 horsepower to lift 100 kg by 10 m in 5 seconds. That's roughly the power of a high-end electric scooter motor or a strong human athlete sprinting.

Step 4 — What if it took half as long?

If the same lift happened in 2.5 seconds instead:

$P = \dfrac{9810}{2.5} = 3924\;\text{W} \approx 5.26\;\text{hp}$

Same energy, doubled rate, doubled power. Power and time are inversely proportional for a fixed amount of work.

Step 5 — How does power relate to force and velocity?

For an object moving at speed $v$ being pushed by force $F$ in the direction of motion:

$P = F\,v$

This is the instantaneous power. For the motor lifting at constant speed $v = 10/5 = 2\;\text{m/s}$ with the lifting force $F = mg = 981\;\text{N}$:

$P = (981)(2) = 1962\;\text{W} \;\;\checkmark$

Both methods agree.

---

Answer:

$\boxed{\;P = \dfrac{W}{t} = \dfrac{mgh}{t} = 1962\;\text{W} \approx 2.63\;\text{hp}\;}$

The motor delivers an average of 1962 watts (about 2.6 horsepower) to lift 100 kg by 10 meters in 5 seconds.

Try It

• Adjust the mass, height, and time sliders.
• Notice that doubling the time halves the power (same work, slower delivery).
• Watch the elevator visualization rise faster or slower as you change the time.
• The HUD shows both the work and the resulting power in watts and horsepower.