Uniform Acceleration: worked example
| Initial speed (m/s) | 5 |
|---|---|
| Acceleration (m/s²) | 2 |
| Time (s) | 10 |
| Final speed (m/s) | 25 |
| Distance covered (m) | 150 |
| Average speed (m/s) | 15 |
Common error: Multiplying the final speed by the time. That treats the object as if it had been at full speed the whole way and overstates the distance.
Uniform Acceleration: formula
Real accelerations vary with engine power, drag and grade, so the result holds only for short spans or ideal cases. Speeds and distances must use the same unit system. Negative results, such as a negative final speed, mean the object reversed.
Very high speeds need relativistic treatment.
Enter the initial speed in meters per second, the constant acceleration in meters per second squared and the time in seconds. The final speed is the initial speed plus acceleration times time, and the distance is initial speed times time plus half the acceleration times the time squared. Use a negative acceleration for slowing down.
The formulas assume the acceleration stays constant for the whole interval.
Uniform Acceleration: changing Initial speed (m/s)
| 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 (example) | 25 | 150 | 15 |
| 5.5 | 25.5 | 155 | 15.5 |
| 6 | 26 | 160 | 16 |
Uniform Acceleration: compare input ranges
| Input | Tested from | To | Final speed (m/s): low input | Final speed (m/s): high input | Swing |
|---|---|---|---|---|---|
| Acceleration (m/s²) | 1.8 | 2.2 | 23 | 27 | 4 (16%) |
| Time (s) | 9 | 11 | 23 | 27 | 4 (16%) |
| Initial speed (m/s) | 4.5 | 5.5 | 24.5 | 25.5 | 1 (4.0%) |
Uniform Acceleration: individual input comparisons
| Input | Value | Final speed (m/s) | Distance covered (m) | Average speed (m/s) |
|---|---|---|---|---|
| Initial 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 | |
| Acceleration (m/s²) | 1.6 | 21 | 130 | 13 |
| 1.8 | 23 | 140 | 14 | |
| 2 | 25 | 150 | 15 | |
| 2.2 | 27 | 160 | 16 | |
| 2.4 | 29 | 170 | 17 | |
| Time (s) | 8 | 21 | 104 | 13 |
| 9 | 23 | 126 | 14 | |
| 10 | 25 | 150 | 15 | |
| 11 | 27 | 176 | 16 | |
| 12 | 29 | 204 | 17 |
Uniform Acceleration: combined input changes
| Initial speed (m/s) / Acceleration (m/s²) | 1.6 | 2 | 2.4 |
|---|---|---|---|
| 4 | 20 | 24 | 28 |
| 4.5 | 20.5 | 24.5 | 28.5 |
| 5 | 21 | 25 | 29 |
| 5.5 | 21.5 | 25.5 | 29.5 |
| 6 | 22 | 26 | 30 |
Uniform Acceleration: which assumptions move the result?
Uniform Acceleration: values and definitions
| Quantity and definition | Value used |
|---|---|
| Initial speed (m/s) | 5 |
| Acceleration (m/s²) | 2 |
| Time (s) | 10 |
| Final speed (m/s) | 25 |
| Distance covered (m) | 150 |
| Average speed (m/s) | 15 |
Uniform Acceleration: half and double Acceleration (m/s²)
| Acceleration (m/s²) | Final speed (m/s) |
|---|---|
| 1 | 15 |
| 2 | 25 |
| 4 | 45 |
Physics & Mechanics calculators: Hooke's Law Calculator, Ideal Gas Law Calculator, Gravitational Potential Energy Calculator, Work and Power Calculator, Wavelength and Frequency Calculator, Projectile Motion Calculator.
With a steady acceleration, speed grows in a straight line and distance grows as a curve. Starting at 5 meters per second and gaining 2 meters per second every second, an object is moving at 25 after 10 seconds. It has covered 150 meters, because the average speed over the run was 15, not 25.
The distance depends on that average, which is the point most people miss.
Confirm the acceleration is constant. A car pulling away in gears is not, and these formulas describe a smooth, steady change.
See the speed relation on the speed, distance and time calculator, the falling case on the free fall calculator and the energy on the kinetic energy calculator. The projectile motion and force pages cover related problems, and the pace and unit converters handle units.
How do I find the acceleration from two speeds?
Subtract the initial speed from the final speed and divide the difference by the time taken over that change.
Does the formula work when slowing down?
Yes, using a negative acceleration, as long as you stop the calculation before the object reverses.
What are the equations of uniform acceleration?
Final velocity is u + at. Displacement is ut + ½at². Both equations assume constant acceleration and a consistent signed direction.
Use matching time and distance units before substituting the initial velocity u, acceleration a and elapsed time t.