Kinetic & potential energy
The idea
Energy is the ability to make things happen, and two of its most useful forms have to do with motion and position. Kinetic energy is the energy of a moving object: kinetic energy = 1/2 × mass × speed², measured in joules (J). Gravitational potential energy is stored by lifting something against gravity: potential energy = mass × gravitational strength × height, also in joules. A drawn bowstring or a stretched spring stores elastic potential energy the same way — energy parked in position, waiting to become motion.
The detail most people miss is that little ² on the speed. Because speed is squared, doubling your speed does not double kinetic energy — it quadruples it, and tripling speed makes it nine times larger. This is not a math curiosity: it is why a car crash at 60 km/h is four times more violent than one at 30 km/h, and why stopping distances grow so fast. Whenever speed changes in a problem, expect the energy to change much more dramatically than your gut suggests.
Worked example
A 40 kg student rides a skateboard at 3 m/s. Find her kinetic energy, then find it again when she speeds up to 6 m/s. How do the two compare?
- Use kinetic energy = 1/2 × mass × speed². First square the speed: 3 × 3 = 9.
- Multiply through: 0.5 × 40 kg × 9 = 180 J at 3 m/s.
- Now at the doubled speed: 6 × 6 = 36, so kinetic energy = 0.5 × 40 × 36 = 720 J.
- Compare the two: 720 ÷ 180 = 4. Doubling the speed quadrupled the kinetic energy, because the speed gets squared before anything else happens.
- Sanity-check the scale: 720 J is about the energy needed to lift this same 40 kg student 1.8 m straight up, since 40 × 10 × 1.8 = 720 J — substantial for a skateboarder, but nothing like a lightning bolt.
Answer. She has 180 J of kinetic energy at 3 m/s and 720 J at 6 m/s — four times as much, not twice.
Check your understanding
- Why does doubling an object's speed quadruple its kinetic energy, while doubling its mass only doubles it?
- Where in a playground swing's path is potential energy largest, where is kinetic energy largest, and how do you know?
- How would you estimate which has more kinetic energy: a slow-moving truck or a fast-moving bicycle, and what numbers would you need?
- What everyday objects store potential energy right now around you, and what would have to happen to release it?
Build the foundations first
Kinetic & potential energy builds on these concepts. If any feel shaky, start there.