Speed, distance and time
Average speed is total distance divided by total time, stops included. A trip of 120 miles in two and a half hours averaged 48 mph. Trip-average speed equals total distance divided by total elapsed time.
Each leg contributes its own distance and duration. Driving out at 60 and back at 40 averages 48, not 50.
Constant acceleration
With a steady acceleration, speed grows in a straight line and distance grows with the square of time. Starting at 5 meters per second and gaining 2 meters per second every second, an object reaches 25 meters per second after 10 seconds and has covered 150 meters. The average speed over the run, 15, is what turns time into distance.
Falling objects
Without air resistance, an object dropped from rest falls a distance that grows with the square of time, and every object falls the same way regardless of mass. From 50 meters it lands in about 3.2 seconds at about 31 meters per second. Real objects are slowed by air, and a light object with a large area falls far more slowly.
Energy and power have different units
Assume a 75 kg mass at 10 m/s: kinetic energy is ½ × 75 × 10² = 3,750 J. Power is energy per unit time; an assumed constant 250 W for 120 seconds transfers 30,000 J. Those are model calculations, not a claim about a person’s capability or a machine’s efficiency.
Changing mass scales kinetic energy linearly, while doubling speed multiplies it by four.
Force and mass
Force equals mass times acceleration. A 70 kilogram person under standard gravity presses down with about 687 newtons. Mass is how much matter there is, and weight is the force gravity puts on it, so the same mass weighs about a sixth as much on the Moon.
Do not use pounds of mass in a formula that expects kilograms.
Energy of motion
Kinetic energy is half the mass times the speed squared. Doubling the speed quadruples the energy, which is why crashes at higher speeds are so much more severe and why stopping distances lengthen quickly. A 1,500 kilogram car at 25 meters per second carries 468,750 joules.
Work and power
Work is force times the distance moved along the force, and only the component along the motion counts. A 50 newton pull at 30 degrees over 12 meters does about 520 joules. Power is work divided by time, so doing that work in 4 seconds is about 130 watts.
One mechanical horsepower is about 745.7 watts.
Moving in a circle
Motion along a curve needs a force toward the center, the centripetal force, equal to mass times speed squared over the radius. A 1,200 kilogram car at 20 meters per second in a 50 meter turn needs 9,600 newtons, from tire friction. The outward push you feel is inertia, not a real force.
Know when the textbook model fails
These formulas ignore air resistance, friction, wind, spin and changes in gravity. That is fine for a first estimate and poor for a fast, light or spinning object. When the stakes are high, such as structural loads or safety, use a professional analysis and treat the calculator as a check on the arithmetic.
Assumed inputs and calculated outputs
Uniform Acceleration Calculator: input sensitivity
| Initial speed (m/s) | Final speed (m/s) | Distance covered (m) | Average speed (m/s) |
|---|---|---|---|
| 4 | 24 | 140 | 14 |
| 4.5 | 24.5 | 145 | 14.5 |
| 5 | 25 | 150 | 15 |
| 5.5 | 25.5 | 155 | 15.5 |
| 6 | 26 | 160 | 16 |
Open the Uniform Acceleration Calculator to use your own numbers →
What goes wrong
Physics formulas for everyday questions: common errors
| The mistake | Why it misleads | Do this instead |
|---|---|---|
| Mixing units | Miles per hour or pounds in a metric formula give an answer off by a fixed factor. | Convert to meters, kilograms and seconds first. |
| Averaging two speeds by adding and halving | More time is spent at the slower speed, so the simple mean is too high. | Divide total distance by total time. |
| Doubling the energy for double the speed | Kinetic energy depends on speed squared, so doubling speed quadruples it. | Use half the mass times the speed squared. |
| Expecting the ideal range in real life | Air resistance shortens a throw and lowers the best angle. | Treat the result as an upper bound for a fast or light object. |
Physics formulas for everyday questions: worked calculation
Using the Uniform Acceleration Calculator worked example, moving Initial speed (m/s) from 4 to 6 changes the Final speed (m/s) from 24 to 26.
| Input | Value | Definition |
|---|---|---|
| Initial speed (m/s) | 5 | Entered example assumption. |
| Acceleration (m/s²) | 2 | Entered example assumption. |
| Time (s) | 10 | Entered example assumption. |
| Final speed (m/s) | 25 |
|---|---|
| Distance covered (m) | 150 |
| Average speed (m/s) | 15 |
| Initial speed (m/s) | Final speed (m/s) | Distance covered (m) | Average speed (m/s) |
|---|---|---|---|
| 4 | 24 | 140 | 14 |
| 4.5 | 24.5 | 145 | 14.5 |
| 5 | 25 | 150 | 15 |
| 5.5 | 25.5 | 155 | 15.5 |
| 6 | 26 | 160 | 16 |
Which input moves the final speed (m/s) most in the uniform acceleration calculator?
Ranked by how far each moves the final speed (m/s) across the range tested: acceleration (m/s²) (4, 16%), time (s) (4, 16%) and initial speed (m/s) (1, 4.0%).
If I double acceleration (m/s²) in the uniform acceleration calculator, does the final speed (m/s) double?
Doubling it from 2 to 4 takes the final speed (m/s) from 25 to 45, which is 1.80 times the worked-example figure. So it grows, but by less than double. Halving it to 1 gives 15.
Physics formulas for everyday questions: points to carry forward
- Convert to meters, kilograms and seconds before you use any formula.
- Average speed weights the legs by their elapsed times. An unweighted mean works only when the time spent at each speed is equal.
- Kinetic energy grows with the square of speed, so speed matters more than mass.
- On level ground with no air, 45 degrees gives the longest projectile range.
- The formulas ignore air resistance and friction, so real results are lower.
How do I calculate average speed?
Divide the total distance by the total time, including any stops. The speed, distance and time calculator does the division.
How do I find how long an object takes to fall?
Take the square root of twice the height divided by 9.81, with the height in meters. The free fall calculator gives the time and the impact speed.
What launch angle gives the longest range?
About 45 degrees on level ground with no air resistance.
What is the difference between mass and weight?
Mass is the amount of matter in kilograms. Weight is the force gravity exerts on it, in newtons.
Why does speed matter so much for crash severity?
Kinetic energy grows with the square of speed, so a small rise in speed adds a lot of energy.
What is centripetal force?
The inward force needed to keep an object moving in a circle. It equals mass times speed squared over the radius.
How do I convert horsepower to watts?
Multiply by about 745.7 for mechanical horsepower. The power converter handles the different horsepower definitions.
Does mass change how fast something falls?
Not without air resistance. A heavy and a light object dropped together land together, and the difference in real life comes from air pushing on the larger surface.
What is the difference between speed and velocity?
Speed is how fast an object moves. Velocity is speed in a given direction, so a car circling a track at a steady speed has a changing velocity.
How much energy does lifting something store?
Potential energy is mass times gravity times height. Ten kilograms lifted 5 meters stores about 490 joules, which it gives back if it falls.
What is the difference between work and power?
Work is the energy transferred by a force over a distance. Power is how fast that work is done, so the same work done faster needs more power.