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Topic 3.5: Practice Sheet — Power

Name: _______________________________ Date: _______________ Period: ______

Directions: Write the power formula you're using before substituting ($P=W/t$, $P=Fd/t$, or $P=Fv$), keep units on every line, and use $g=10\text{ m/s}^2$. Show every step.

Warm-Up Level (straightforward, one-step)

  1. A $50\text{ kg}$ student climbs $3.0\text{ m}$ of stairs in $5.0\text{ s}$. Find the average power.
  2. A motor lifts a $100\text{ kg}$ crate at a constant speed of $0.50\text{ m/s}$. Find the power the motor delivers.
  3. An engine delivers $150\text{ kW}$. Convert this to horsepower ($1\text{ hp}=746\text{ W}$).

Standard Level (multi-step, matches typical AP Classroom depth)

  1. A rower performs four trials, recording the average force on the boat, the distance traveled, and the time. Find the average power for each trial and state which is greatest.

    Trial$F_{avg}$$d$$\Delta t$
    A$180\text{ N}$$50\text{ m}$$45\text{ s}$
    B$240\text{ N}$$30\text{ m}$$30\text{ s}$
    C$210\text{ N}$$45\text{ m}$$35\text{ s}$
    D$260\text{ N}$$35\text{ m}$$40\text{ s}$

  2. A $2.0\text{ kg}$ block is pulled at a constant $2.0\text{ m/s}$ up a frictionless $30°$ ramp, and an identical block up a frictionless $60°$ ramp at the same speed. Find the power delivered to each.

  3. A $2.0\text{ kg}$ box starts at rest and is pulled with constant acceleration, traveling $9.0\text{ m}$ in $3.0\text{ s}$. Find the average power. Then show it matches $\dfrac{2md^2}{t^3}$.

  4. Two crates rest on a flat surface. A student applies the same constant force $F$ over the same distance $d$ to each; the first takes time $t$ and the second takes $t/2$. Find the ratio of the average powers $P_2:P_1$.

AP-Level (multi-part: calculate + justify/represent/predict-a-change)

  1. A $3.0\text{ kg}$ block starts from rest and accelerates at a constant rate; after $2.0\text{ s}$ its speed is $4.0\text{ m/s}$. a) Find the average power over the 2.0 s. b) Find the instantaneous power at $t=2.0\text{ s}$. c) Explain, using $P=Fv$, why the final power is larger than the average.
  2. At time $t_1$ a train on a level track has speed $v$ and acceleration $a$. At $t_2$ it has speed $2v$ and acceleration $a$. Compare the instantaneous power $P_2$ to $P_1$ and justify.

Progress Check Style (evaluate the method — AP Classroom format)

  1. Figure 1 shows power delivered to an object falling linearly from $6\text{ W}$ to $2\text{ W}$ over $4\text{ s}$ (energy change $\Delta E_1$). Figure 2 shows power rising linearly from $2\text{ W}$ to $6\text{ W}$ over the same 4 s (energy change $\Delta E_2$). Which correctly compares $\Delta E_1$ and $\Delta E_2$ with a valid justification? (A) $\Delta E_1<\Delta E_2$, because the final power in Figure 1 is smaller. (B) $\Delta E_1<\Delta E_2$, because the slope is negative in Figure 1 and positive in Figure 2. (C) $\Delta E_1=\Delta E_2$, because the area under each graph is the same. (D) $\Delta E_1=\Delta E_2$, because the magnitude of the slope is the same in both graphs.
  2. A box of mass $m$ starts at rest and is pulled to the right a distance $d$ in time $t$ with constant acceleration. Which is the average power delivered to the box? (A) $\dfrac{2md^2}{t^2}$ (B) $\dfrac{2md^2}{t^3}$ (C) $\dfrac{md^2}{2t^2}$ (D) $\dfrac{md^2}{2t^3}$

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.