Four formulas, depending on what you know
Acceleration is the rate that velocity changes, measured in m/s². Which equation you reach for depends on the data you have in hand — velocities and time, force and mass, or a distance.
| You know | Formula | Solves for |
|---|---|---|
| Start & end speed, time | a = (v − u) ÷ t | Everyday acceleration |
| Force and mass | a = F ÷ m | Newton's second law |
| Speeds and distance | v² = u² + 2as | a with no time given |
| Free fall from rest | a = g = 9.81 | v and drop distance |
Here u is the starting velocity, v the final velocity, t the time, s the distance, F the net force and m the mass. Each one rearranges to solve for any single unknown.
The two you use most
Change in velocity over time. From 0 to 60 mph (26.82 m/s) in 5 s is 26.82 ÷ 5 = 5.36 m/s². Rearranged: v = u + at, or t = (v − u) ÷ a.
Newton's second law. A 10 N force on a 2 kg object gives 5 m/s². Rearranged: F = ma, or m = F ÷ a. Force and acceleration can be negative when they point backward — that is braking.
Reference points to sanity-check a result
| Situation | Acceleration | In g |
|---|---|---|
| Earth's gravity (g) | 9.81 m/s² | 1.0 |
| Moon's gravity | 1.62 m/s² | 0.17 |
| Sports car, 0–60 in 5 s | 5.36 m/s² | 0.55 |
| Tesla Plaid, 0–60 in ~2 s | ~13.4 m/s² | ~1.37 |
| F1 car braking | ~50 m/s² | ~5 |
Quick check: to read m/s² as g-force, divide by 9.81 (roughly, divide by 10). The kinematic formulas only hold while acceleration stays constant.
What people get wrong
- Fast is not accelerating. Constant speed means zero acceleration, however high the speed.
- 0–60 mph is not 0–100 km/h. 60 mph is 96.6 km/h, so the two benchmarks give different numbers — convert before comparing.
- Free fall ignores air. The 9.81 m/s² figure assumes a vacuum; real objects hit a terminal velocity as drag builds.
Common questions
How do you calculate acceleration?
Divide the change in velocity by the time it took: a = (v - u) divided by t. Going from 0 to 26.82 m/s (0 to 60 mph) in 5 seconds gives 5.36 m/s squared.
What is the difference between acceleration and velocity?
Velocity is how fast something moves; acceleration is how fast that velocity is changing. A car holding a steady 70 mph has high velocity but zero acceleration.
Is deceleration the same as negative acceleration?
Yes. Slowing down is just acceleration with a minus sign. A car braking from 100 km/h to a stop in 5 seconds has an acceleration of about -5.56 m/s squared.
What does 1 g of acceleration feel like?
1 g is 9.81 m/s squared, the same pull as normal gravity, so it feels like your own body weight pressing you into the seat. Roller coasters hit 3 to 6 g; fighter pilots train for up to 9 g.
