Physics 1 · Unit 4: Energy · 14 min read · Updated 2026-05-11
AP Physics 1 Work and Kinetic Energy — AP Physics 1
AP Physics 1 · Unit 4: Energy · 14 min read
1. Mechanical Work by a Constant Force★★☆☆☆⏱ 4 min
W = \vec{F} \cdot \vec{d} = Fd\cos\theta
Where $\theta$ is the angle between the force and displacement vectors, and the SI unit of work is the joule ($1\ \text{J} = 1\ \text{N} \cdot \text{m}$). Only the component of force parallel to displacement does work. Perpendicular components do zero work because $\cos 90^\circ = 0$. Work is positive when energy is added to the object ($\theta < 90^\circ$) and negative when energy is removed ($\theta > 90^\circ$). Net work is the algebraic sum of work done by all individual forces.
Exam tip: Always confirm which axis the problem's given angle is measured from. If the angle is given from the vertical instead of the horizontal, use $\sin\theta$ instead of $\cos\theta$ to get the parallel component of force.
2. Kinetic Energy and the Work-Energy Theorem★★☆☆☆⏱ 4 min
This theorem is a powerful alternative to Newtonian kinematics for problems relating speed and displacement, eliminating the need to calculate acceleration first.
Exam tip: If a problem gives displacement and asks for speed, always check if the work-energy theorem is faster than kinematics. It will save you 1-2 minutes on most MCQ questions.
3. Work Done by a Variable Force★★★☆☆⏱ 3 min
When force varies with position (e.g., spring force, changing applied force), the constant-force work formula does not apply. For AP Physics 1, work done by a variable force is equal to the total area under a force vs. position ($F$ vs. $x$) graph between the initial and final position.
Exam tip: If the force crosses from positive to negative on the $F-x$ graph, don't forget to subtract the area of the negative region, don't just add all areas regardless of sign.
4. Power★★☆☆☆⏱ 3 min
Average power over a time interval $\Delta t$ is given by:
P_{\text{avg}} = \frac{W}{\Delta t}
For instantaneous power (power at a specific moment), when force $F$ is parallel to velocity $v$, the formula simplifies to:
P = Fv
This is commonly used for problems involving engines, vehicles, or human movement where power output is given.
Exam tip: Always convert kilowatts to watts (multiply by 1000) before calculating energy or time. A common mistake leaves power in kilowatts and gets a time 1000 times smaller than the correct value.
Common Pitfalls
Why: Students memorize the simplified $W=Fd$ for parallel forces and forget to adjust for angled forces.
Why: Students confuse "work done by the applied force" with "net work from all forces".
Why: Students are used to working with velocity and force vectors, so they carry over vector addition to kinetic energy.
Why: Students remember "area equals work" but forget force direction changes the sign.
Why: Students memorize the simplified power formula and use it for any problem.