Velocity Calculator
Enter any two values to find the third. Leave the unknown field blank.
Enter any 3 of the 5 SUVAT variables and leave the unknowns blank. The calculator will find them.
SUVAT Equations Reference
All five SUVAT equations, valid for uniform (constant) acceleration in a straight line.
| Equation | Variables Used | Missing Variable |
|---|---|---|
| v = u + at | u, a, t → v | s (displacement) |
| s = ut + ½at² | u, a, t → s | v (final velocity) |
| v² = u² + 2as | u, a, s → v | t (time) |
| s = ½(u + v)t | u, v, t → s | a (acceleration) |
| s = vt − ½at² | v, a, t → s | u (initial velocity) |
s = displacement (m) | u = initial velocity (m/s) | v = final velocity (m/s) | a = acceleration (m/s²) | t = time (s)
Common Velocity Reference Values
Understanding Velocity and Motion
Velocity is a fundamental concept in Newtonian mechanics, appearing in almost every branch of physics and engineering. Understanding the difference between scalar and vector quantities, and being able to apply the SUVAT equations, is essential for UK GCSE and A-Level Physics examinations.
Scalar vs Vector: Speed and Velocity
In physics, we distinguish carefully between quantities with direction (vectors) and those without (scalars). Speed is a scalar — it tells you only how fast something is moving. A car travelling at 60 mph is described by its speed alone. Velocity is a vector — it requires both magnitude and direction. "60 mph due north" is a velocity. This distinction matters enormously: two cars travelling at the same speed in opposite directions have the same speed but completely different velocities.
Displacement is similarly the vector counterpart of distance. If you walk 500 m east and then 500 m west, your total distance is 1,000 m, but your displacement is 0 m (you are back where you started). Average velocity uses displacement; average speed uses total distance.
The Basic Velocity Equation: v = d/t
For motion at constant speed (uniform motion), the relationship is simple: v = d / t. This allows us to calculate any one of the three quantities if the other two are known. Common rearrangements: d = v × t (distance = speed × time) and t = d / v (time = distance ÷ speed).
In real-world problems, be careful with units. Speed in m/s requires distance in metres and time in seconds. To convert between units: 1 km/h = 1/3.6 m/s = 0.278 m/s; 1 mph = 0.447 m/s; 1 m/s = 3.6 km/h = 2.237 mph.
SUVAT Equations Explained
The SUVAT equations apply when acceleration is constant (uniform). The five variables are: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). Given any three, you can derive the other two using the four equations. The equations are derived from the definition of acceleration and the area under a velocity-time graph.
Worked SUVAT Example
A car accelerates from rest (u = 0) to 30 m/s with acceleration a = 3 m/s². Find the time taken and distance covered.
- Using v = u + at: 30 = 0 + 3t ⇒ t = 10 s
- Using s = ut + ½at²: s = 0 + ½ × 3 × 100 = 150 m
- Verification: v² = u² + 2as = 0 + 2 × 3 × 150 = 900 ⇒ v = 30 m/s ✓
Free Fall and Projectile Motion
Free fall under gravity is a classic SUVAT problem. With u = 0, a = g = 9.81 m/s² (downward): v = gt (velocity after time t), s = ½gt² (distance fallen). For projectile motion, horizontal and vertical components are treated independently: horizontal motion is uniform (no acceleration), vertical motion uses SUVAT with a = g.
Velocity-Time Graphs
On a velocity-time (v-t) graph: the gradient (slope) represents acceleration; the area under the graph represents displacement. A horizontal line means constant velocity (zero acceleration). A straight sloped line means uniform acceleration. The SUVAT equations correspond directly to geometric properties of these graphs.
Units of Velocity in the UK
In physics calculations, SI units are standard: m/s (metres per second). In everyday UK life, speed is commonly given in mph (miles per hour) for road travel, and km/h is used in science and international contexts. The UK national speed limits are 30 mph in built-up areas, 60 mph on single carriageways, and 70 mph on motorways and dual carriageways.