Uniformly Decelerated Motion calculator

Type v₀ [m/s] and deceleration a [m/s²] as a positive number. The calculator computes s_ham = v₀²/(2a) and t_stop = v₀/a: 14 m/s and 7 m/s² is 14 m and 2 s. No reaction time t_r.

Inputs

Result

Initial speed v₀, Deceleration a (positive) and Time t (optional). The result shows up here.

How it works

v₀ v→0 STOP s_ham = v₀²/(2a)
Deceleration a > 0 brings speed to zero over braking distance s_ham.

Constant braking: type a as a positive number, s = v₀²/(2a), t_stop = v₀/a. 14 m/s (about 50 km/h) and 7 m/s²: s = 196 / 14 = 14 m, t = 2 s. The US examples use 13.4 m/s (about 30 mph) and 6 m/s²: s ≈ 15.0 m, t ≈ 2.23 s. 26.8 m/s and 6 m/s²: s ≈ 59.9 m, t ≈ 4.47 s. 31.3 m/s and 8 m/s²: s ≈ 61.2 m, t ≈ 3.91 s. 5 m/s and 2 m/s²: s = 6.25 m, t = 2.5 s. 14 m/s and 2 m/s²: s = 49 m, t = 7 s.

50 in an m/s field is 180 km/h, not 50 km/h. Type 50 km/h as 13.9, or 30 mph as 13.4. 11 m/s and 1.2 m/s²: s ≈ 50.4 m, t ≈ 9.17 s. 6 m/s and 2.5 m/s²: s = 7.2 m, t = 2.4 s. Optional t gives v(t) = v₀ - a t while t ≤ t_stop. Example: 26.8 m/s, 5 m/s² and t = 2 s is v = 16.8 m/s, still before a stop.

Fields: v₀ in m/s, positive a in m/s², optional t in seconds. Blank t means s and t_stop, not the state at time t. a = 0 does not stop you. v₀ and a both need a number before 14 m can appear. A comma and a period are the same a: 7,5 and 7.5. Do not type -7: the calculator needs a positive deceleration.

Distance with reaction time t_r is on stopping distance: s = v t_r + v²/(2a). Here you count from the moment you hit the pedal. Speeding up lives on accelerated motion. SUVAT will take a negative a if you prefer the sign inside a triple of inputs.

F = m a while braking is on the force page. Here it is kinematics, s and t, with no mass. Impulse J = Δp is another calculator.

Type 14 and 7, click Calculate, and match 14 m and 2 s. Then 13.4 and 6. The header symbol does not press the pedal. Stopping distance is s_ham in this formula.

With reaction time: stopping distance. Speeding up: accelerated motion.

How to use

  1. Type v₀ in m/s, for example 14. 50 km/h is 13.9 m/s; about 30 mph is 13.4. Not 50 in an m/s field.
  2. Type positive a, for example 7 m/s². Do not type -7.
  3. Leave t blank for s and t_stop, or type a moment for v(t) = v₀ - a t.
  4. Click Calculate. 14 and 7 give 14 m and 2 s. 26.8, 5 and t = 2 give v = 16.8 m/s.
  5. With reaction time, open stopping distance. Speeding up is on accelerated motion.

Formula

sbrake = v02 / (2a)

tstop = v0 / a

v(t) = v0 − a t (for t ≤ tstop)

Deceleration a is positive.

Braking s_ham, v₀, and a to a full stop

From the pedal, no t_r: s_ham = v₀²/(2a) and t_stop = v₀/a. 14 m/s and 7 m/s² is 14 m and 2 s. Type a as positive.

v₀
Speed at the start of braking [m/s]. 14 m/s at a = 7 m/s² gives s_ham = 14 m.
a
Positive deceleration [m/s²]. The calculator subtracts: v(t) = v₀ minus a t, while t ≤ t_stop.
t
Optional time [s]. Blank t leaves s_ham and t_stop. t longer than t_stop does not reverse.
s_ham
Braking distance from the pedal [m]. 14² / 14 = 14 m. No t_r from stopping distance.

Real-life examples

Example 1

v₀ = 13.4 m/s, a = 6 m/s²: distance and stop time.

Example 2

v₀ = 26.8 m/s, a = 6 m/s².

Example 3

v₀ = 31.3 m/s, a = 8 m/s².

Example 4

v₀ = 5 m/s, a = 2 m/s².

Example 5

v₀ = 11 m/s, a = 1.2 m/s².

Example 6

v₀ = 26.8 m/s, a = 5 m/s², t = 2 s.

Example 7

v₀ = 6 m/s, a = 2.5 m/s².

Example 8

v₀ = 14 m/s, a = 2 m/s².

Ways to use this calculator

  • You compute stop distance at 14 m/s and 7 m/s².
  • You compare this s with stopping distance, which adds t_r.

Related calculators

Stopping distance
Adds thinking time t_r. 14 m/s and 7 m/s² without t_r is 14 m
Momentum before braking
Momentum just as braking begins.
Work done by braking
Work of the braking force over the stopping distance.
Kinetic energy to scrub off
Kinetic energy grows with speed squared.
Uniformly Accelerated Motion
Distance and final speed at constant acceleration.
Uniform Motion Calculator
Solve any of speed, distance or time at constant speed.

All physics calculators

Frequently asked questions

How much s and t at 14 m/s and a = 7 m/s²?

Braking distance s_ham is 14 m, stop time t_stop is 2 s. That is 14² / (2 × 7) = 196 / 14 and 14 / 7. From the pedal, not from noticing the hazard.

Should I type negative a?

No. Here a is positive: I brake at 7 m/s², not minus 7. A signed a belongs on the SUVAT page.

Which units do I type?

Speed v₀ [m/s], deceleration a [m/s²], optional time t [s]. Results s_ham [m] and t_stop [s]. Convert 50 km/h to about 13.9 m/s first.

Is 50 in the field 50 km/h?

Not if the label is m/s. Typed 50 is 180 km/h. Fifty kilometres per hour is about 13.9 m/s. About 30 mph is 13.4 m/s.

How is this different from stopping distance?

Here there is no t_r. There s = v t_r + v²/(2a), with reaction. Here you start at the pedal, constant a only.

What is optional t for?

For v(t) = v₀ minus a t, while t does not pass t_stop. At 26.8 m/s, 5 m/s² and 2 s you get 16.8 m/s, not a reverse drive underground.

How much at 13.4 m/s and 6 m/s²?

You get s_ham about 15.0 m and t_stop about 2.23 s. At 5 m/s and 2 m/s²: s_ham = 6.25 m, t_stop = 2.5 s.

Does a comma in 7.5 work?

Yes. 7.5 and 7,5 are the same a [m/s²]. A comma and a period mean the same value.

Where is F = m a while braking?

On the F = m·a page. There mass and acceleration give force. Here it is kinematics: s_ham and t_stop, with no mass field.

How much at 14 m/s and 2 m/s²?

Distance s_ham is 49 m, t_stop is 7 s. Weaker a at the same v₀ stretches both the path and the time to a stop.

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.