Example 1
v₀ = 0, a = 3.5 m/s², t = 8 s: distance and vₖ.
Uniformly Accelerated Motion calculator
Enter v₀, constant acceleration a, and time t. The calculator computes distance s = v₀ t + ½ a t² and vₖ = v₀ + a t. From rest at 3.5 m/s² for 8 s you get 112 m and 28 m/s, about 101 km/h.
Result
Initial speed v₀, Acceleration a and Time t. The result shows up here.
How it works
With constant a, two formulas apply together: s = v₀ t + ½ a t² and vₖ = v₀ + a t. Start from rest shortens them to s = ½ a t² and vₖ = a t. A compact at 3.5 m/s² for 8 s: s = ½ × 3.5 × 64 = 112 m, vₖ = 28 m/s, which is 100.8 km/h, about 101. At v₀ = 0, a = 1.2 m/s², and t = 10 s you get 60 m and 12 m/s, as on the second card.
Fields: v₀, a, t. Units from the labels: m/s, m/s², seconds. The result is s in meters and vₖ in m/s. Blank v₀ is usually taken as zero, start from rest. Without a or t there is nothing to build ½ a t² from. A comma and a period are the same a: 3,5 and 3.5.
a stays constant for the whole t. That is not a one-pair Δv/t: that a lives on the acceleration page. Here the triple (v₀, a, t) gives distance and final speed. Negative a is braking; the sibling card is decelerated motion. F = m a is on the force page: here it is kinematics, not newtons.
Once v₀ is not zero, the formula does not shrink to ½ a t². Rolling onto flat ground at 5 m/s, then a = 0.8 m/s² for 6 s: s = 5 × 6 + ½ × 0.8 × 36 = 44.4 m, vₖ = 5 + 4.8 = 9.8 m/s. v₀ = 2 m/s, a = 1.5 m/s², t = 4 s gives 20 m and 8 m/s.
A long time at small a is on the pages too: v₀ = 0, a = 0.55 m/s², t = 80 s is s = 1760 m and vₖ = 44 m/s. v₀ = 0, a = 2 m/s², t = 35 s is 1225 m and 70 m/s. A short burst: 4.5 m/s² for 2 s from rest is 9 m and 9 m/s.
Type 0, 3.5, and 8, click Calculate, and match 112 m and 28 m/s. Then 0, 1.2, and 10, then 5, 0.8, and 6. The header symbol does not press the pedal. Stopping distance with t_r lives on its own page.
a = Δv/t alone: acceleration. Braking: decelerated motion.
How to use
- Type v₀ in m/s. Zero if you start from rest. Blank v₀ is usually taken as 0, so a standing start does not need a typed 1.
- Type constant acceleration a, for example 3.5. The label unit is m/s². 3,5 and 3.5 are the same a.
- Type time t in seconds, for example 8. Without t you cannot build ½ a t² or vₖ = v₀ + a t.
- Click Calculate. 0, 3.5, and 8 give 112 m and 28 m/s. 0, 1.2, and 10 give 60 m and 12 m/s. 5, 0.8, and 6 give 44.4 m and 9.8 m/s.
- a = Δv/t alone is on the acceleration page. Braking with t_r is on stopping distance. Here it stays s and vₖ from constant a.
Formula
s = v0t + ½a t2
vk = v0 + a t
For constant acceleration a, time t, and initial speed v0.
s, v₀, vₖ, and a while speeding up
This calculator always takes v₀, a, and t, then computes s and vₖ. Formulas: s = v₀ t + ½ a t² and vₖ = v₀ + a t. Any triple from five lives on the SUVAT page.
- s
- Distance at constant a. Start at v₀ = 0, a = 3.5 m/s², t = 8 s gives s = 112 m, the same set as SUVAT, no field picking here.
- v₀
- Initial speed. Typed 0 is start from rest. Blank will not run: this calculator wants all three inputs.
- vₖ
- Final speed: v₀ + a t. At v₀ = 0, a = 3.5, and t = 8 you get 28 m/s.
- a
- Constant acceleration, positive in the speeding-up sense. Braking with a positive a is on decelerated motion.
- t
- Time speeding up, in seconds. Zero gives s = 0 and vₖ = v₀.
Real-life examples
Example 2
v₀ = 0, a = 1.2 m/s², t = 10 s.
Example 3
Enters the flat at 5 m/s, then a = 0.8 m/s² for 6 s.
Example 4
v₀ = 0, a = 0.55 m/s², t = 80 s.
Example 5
v₀ = 0, a = 2 m/s², t = 35 s.
Example 6
v₀ = 0, a = 4.5 m/s², t = 2 s.
Example 7
v₀ = 0, a = 1.2 m/s², t = 2 s.
Example 8
v₀ = 2 m/s, a = 1.5 m/s², t = 4 s.
Ways to use this calculator
- You compute a run-up: v₀ = 0, a = 3.5 m/s², t = 8 s.
- You compare vₖ with a speed limit after t seconds.
Frequently asked questions
What are s and vₖ at v₀ = 0, a = 3.5 m/s², t = 8 s?
s = ½ × 3.5 × 64 = 112 m. vₖ = 28 m/s, which is 100.8 km/h, about 101. That is the first example card.
How is this different from the acceleration page?
There you compute a = Δv/t from two speeds and a time. Here a is given and constant, and the unknowns are s and vₖ.
Which units do I type?
v₀ in m/s, a in m/s², t in seconds. Result: s in meters, vₖ in m/s. 28 m/s × 3.6 = 100.8 km/h.
What if I leave v₀ blank?
The calculator usually takes blank v₀ as 0, start from rest. Without a or t it will not compute 112 m. Typed 0 is the same standing start.
How much at v₀ = 0, a = 1.2 m/s², t = 10 s?
s = ½ × 1.2 × 100 = 60 m. vₖ = 12 m/s. Second example card.
How much starting at 5 m/s, a = 0.8 m/s², t = 6 s?
s = 5 × 6 + ½ × 0.8 × 36 = 44.4 m. vₖ = 5 + 4.8 = 9.8 m/s. ½ a t² is not enough here, because v₀ is not zero.
Can a be negative?
Negative a is braking at constant deceleration. The calculator uses constant a. The sibling page is decelerated motion, and with t_r it is stopping distance.
How much at v₀ = 0, a = 0.55 m/s², t = 80 s?
s = ½ × 0.55 × 6400 = 1760 m. vₖ = 44 m/s. Longer time, small a, the same pair of formulas.
Where are F = m a and energy at vₖ?
Force is on the F = m·a page. Kinetic energy ½ m v² is on the Ek page once you have vₖ. Here it stays kinematics.
Does a comma in 3.5 work?
Yes. 3,5 and 3.5 are the same a. The calculator does not require a period.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.