Displacement: Velocity and Time
Tap a variable to solve for it, then fill in the other three.
This is a worked example. Change the values, then press Calculate.
ANSWER
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Displacement as a Function of Velocity and Time
One of the core kinematics equations relates displacement to average velocity and time, this calculator solves for any one of the four variables from the other three.
How to use this calculator
- Tap a variable to solve for it: s (displacement), u (initial velocity), v (final velocity), or t (time).
- Fill in the other three known values.
- Read the calculated result and the step-by-step solution.
What this calculator does
This equation, s = ½(u + v)t, calculates displacement as the average of initial and final velocity multiplied by time, one of the standard kinematics (SUVAT) equations for motion under constant acceleration.
s = ½(u + v)t
Why this formula uses average velocity
When acceleration is constant, velocity changes linearly from its initial to final value, meaning the average velocity over the entire time interval is exactly the midpoint between initial and final velocity, (u + v)/2. Multiplying that average velocity by the total time gives the total displacement, which is the intuitive logic behind this formula.
Frequently asked questions
Why does this formula use the average of initial and final velocity?
Under constant acceleration, velocity changes linearly over time, so the average velocity across the whole interval is exactly the midpoint between the initial and final velocities, multiplying that average by time gives total displacement.
Does this formula work if acceleration isn’t constant?
No, this equation assumes constant acceleration, which is standard for basic kinematics problems, if acceleration varies, a different approach (like calculus-based integration) is needed instead.