🧮 Equations of Motion Calculator (SUVAT)

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Use a negative number for slowing down.
Final velocity v (m/s)
0.38
Displacement s (m)
20.38
v² from v² = u² + 2as (m²/s²)
0.1444
Average velocity (m/s)
10.19

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📘 About the Equations of Motion

The three equations of motion describe anything moving in a straight line with constant acceleration. This calculator takes the initial velocity u, acceleration a and time t and works out the final velocity v and the displacement s.

It also checks the third equation, v² = u² + 2as, which links velocity and displacement without time. These are the SUVAT equations taught in Class 9 and Class 11 physics.

🧮 Formula

First equation (velocity–time)
v = u + at
Second equation (position–time)
s = ut + ½at²
Third equation (velocity–position)
v² = u² + 2as

Where

  • u = initial velocity (m/s)
  • v = final velocity (m/s)
  • a = acceleration (m/s², negative when slowing)
  • t = time (s)
  • s = displacement (m)
The equations only hold when acceleration is constant. For free fall use a = 9.81 m/s².

✏️ Worked examples

Accelerating from 5 m/s

You enter
Initial velocity (u)5 m/s
Acceleration (a)2 m/s²
Time (t)10 s
You get
Final velocity v (m/s)25
Displacement s (m)150
v² from v² = u² + 2as (m²/s²)625
Average velocity (m/s)15

After 10 s the velocity is 25 m/s and the displacement is 150 m.

Try this example →

Ball thrown straight up at 20 m/s

You enter
Initial velocity (u)20 m/s
Acceleration (a)-9.81 m/s²
Time (t)2 s
You get
Final velocity v (m/s)0.38
Displacement s (m)20.38
v² from v² = u² + 2as (m²/s²)0.1444
Average velocity (m/s)10.19

After 2 s the ball moves at 0.38 m/s (still rising) and is 20.38 m above the start.

Try this example →

🧭 How to use this calculator

What you enter

  • Initial velocity (u) (m/s)
  • Acceleration (a) (m/s²)Use a negative number for slowing down.
  • Time (t) (s)

What you get

  • Final velocity v (m/s)
  • Displacement s (m)
  • v² from v² = u² + 2as (m²/s²)
  • Average velocity (m/s)

💡 Choosing the right equation

  • No displacement given or needed → v = u + at
  • No final velocity → s = ut + ½at²
  • No time → v² = u² + 2as
  • Starting from rest means u = 0

❓ Frequently asked questions

What are the three equations of motion?

v = u + at, s = ut + ½at² and v² = u² + 2as. They apply to motion in a straight line with constant acceleration.

What does SUVAT stand for?

s = displacement, u = initial velocity, v = final velocity, a = acceleration and t = time.

What is the value of a for free fall?

About 9.81 m/s² downwards. Take upwards as positive and use a = −9.81 m/s² for a ball thrown up.

Can displacement be negative?

Yes. A negative displacement means the object ended up behind its starting point in the direction you chose as positive.