0 to 100 km/h
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v₀ = 0 km/h, v = 100 km/h, t = 6.2 sConvert first: 100 km/h = 100 · 1000/3600 = 27.78 m/s. Then a = (27.78 − 0)/6.2 = 4.48 m/s², a little under half the acceleration of free fall.
Acceleration Calculator
Acceleration from a change in velocity, or from a force and a mass.
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Want to solve these without the calculator?
The Coddy physics course teaches the method: you solve each problem in steps on an interactive board, and it tells you which step went wrong.
The acceleration formula
Acceleration is how quickly a velocity changes. The average acceleration over a time is a = (v − v₀)/t: the final velocity minus the initial velocity, divided by the time the change took. With velocities in m/s and the time in seconds, the answer is in metres per second squared, m/s².
The sign matters. Take the direction of motion as positive, and a negative acceleration means slowing down: a car braking from 25 m/s to a stop in 5 s has a = (0 − 25)/5 = −5 m/s², a deceleration of 5 m/s². If you know the force instead of the velocities, Newton's second law gives a = F/m: a net force of 500 N on a 1200 kg car gives 0.417 m/s².
The calculator has a tab for each way. In the first, fill in any three of acceleration, initial velocity, final velocity and time and it finds the fourth; in the second, any two of acceleration, force and mass. Speeds in km/h, mph or ft/s and masses in grams or pounds are converted to SI units first, and every step of the working is shown.
What to notice
- m/s² reads as metres per second, per second: an acceleration of 3 m/s² adds 3 m/s to the velocity every second.
- A negative acceleration with a positive velocity means slowing down. With a negative velocity it means speeding up the other way, so a minus sign on its own does not mean braking.
- a = (v − v₀)/t gives the average acceleration over the time. If the rate changes along the way, the acceleration at a given moment can be higher or lower.
- In a = F/m, F is the net force: what is left once every push and pull on the object is added up, with directions.
- Near Earth's surface, anything falling freely accelerates at 9.81 m/s², whatever its mass, if air resistance is ignored.
How to calculate acceleration
Find the change in velocity
Final minus initial: v − v₀. From 0 to 100 km/h the change is 100 km/h.
Put it in m/s, and the time in seconds
km/h divide by 3.6, mph multiply by 0.44704. 100 km/h is 27.78 m/s. The calculator does this and shows the factor.
Divide by the time
a = 27.78 / 6.2 = 4.48 m/s².
Check the sign
Positive along the direction you chose, negative against it. Braking while moving forward gives a negative answer.
Typical accelerations
Rounded values from a = (v − v₀)/t for typical figures. A negative value is slowing down.
| Situation | Velocity change | Time | Acceleration |
|---|---|---|---|
| Bus pulling away | 0 to 50 km/h | 15 s | 0.93 m/s² |
| Family car | 0 to 100 km/h | 10 s | 2.78 m/s² |
| Sprinter's start | 0 to 10 m/s | 2 s | 5 m/s² |
| Sports car | 0 to 100 km/h | 3 s | 9.26 m/s² |
| Dropped stone | 0 to 29.43 m/s | 3 s | 9.81 m/s² |
| Car braking hard | 100 km/h to 0 | 4 s | −6.94 m/s² |
Worked examples
Braking to a stop
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v₀ = 25 m/s, v = 0 m/s, t = 5 sa = (0 − 25)/5 = −5 m/s². The minus sign says the acceleration points against the motion: the car loses 5 m/s of speed every second.
From a force and a mass
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F = 500 N, m = 1200 kgIn the force and mass tab, a = F/m = 500 / 1200 = 0.417 m/s². Halve the mass and the same force gives twice the acceleration.
The time to reach a speed
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v₀ = 10 m/s, v = 20 m/s, a = 2 m/s²Leave the time blank: t = (v − v₀)/a = (20 − 10)/2 = 5 s.
Common mistakes
- Subtracting the wrong way round. It is final minus initial, v − v₀; swapping them flips the sign of the answer.
- Mixing km/h with seconds. (100 − 0)/6.2 gives 16.1, which is km/h per second, not m/s². Convert the speeds to m/s first.
- Thinking a negative acceleration always means slowing down. It means the acceleration points the negative way; an object already moving that way speeds up.
- Writing the unit as m/s. Acceleration is in m/s², a change of so many metres per second every second.
- Using one force in a = F/m when several act. Add the forces with their directions, then divide the net force by the mass.
- Using grams in a = F/m. The newton is defined with kilograms, 1 N = 1 kg·m/s², so 500 g goes in as 0.5 kg.
Acceleration FAQ
What is the formula for acceleration?
a = (v − v₀)/t: final velocity minus initial velocity, divided by the time. With velocities in m/s and time in seconds, the answer is in m/s². From rest to 27.78 m/s in 6.2 s is 4.48 m/s².
How do you calculate acceleration from force and mass?
Rearrange Newton's second law, F = ma, to a = F/m. A net force of 500 N on a 1200 kg car gives 500 / 1200 = 0.417 m/s². The force must be in newtons and the mass in kilograms.
What is deceleration?
Acceleration that slows an object down. With the direction of motion as positive it comes out negative: from 25 m/s to rest in 5 s is −5 m/s², a deceleration of 5 m/s².
What is the unit of acceleration?
Metres per second squared, m/s². It means the velocity changes by that many m/s each second. Accelerations are also given in ft/s² (1 ft/s² = 0.3048 m/s²) or as multiples of g, 9.81 m/s².
How do you find acceleration from distance and time?
From rest with constant acceleration, s = ½at² rearranges to a = 2s/t², so 100 m in 10 s gives 2 · 100 / 10² = 2 m/s². With a starting velocity, use s = ut + ½at²; the kinematics calculator solves it.
Is acceleration a vector?
Yes. It has a size and a direction, the direction of the change in velocity. That is why the sign of the answer matters, and why a car turning a corner at a steady speed is still accelerating.
How fast does a falling object accelerate?
At about 9.81 m/s² near Earth's surface, whatever its mass, when air resistance is small. On the Moon it is 1.62 m/s². After 3 s of falling from rest on Earth, the velocity is 29.43 m/s.
