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Displacement calculator icon showing a curved motion path

Displacement as a Function of Velocity, Acceleration and Time

Displacement: Velocity, Acceleration & 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 —

Solution

When acceleration is involved, displacement depends on initial velocity, acceleration, and time together, this calculator solves the standard kinematics equation for any one of the four variables.

How to use this calculator

  1. Tap a variable to solve for it: s (displacement), u (initial velocity), a (acceleration), or t (time).
  2. Fill in the other three known values.
  3. Read the calculated result and the step-by-step solution.

What this calculator does

This equation, s = ut + ½at², calculates displacement from initial velocity, acceleration, and time, one of the standard kinematics (SUVAT) equations for motion under constant acceleration.

s = ut + ½at²

Why solving for time can give two answers

Because time appears squared in this equation, solving for time when displacement, initial velocity, and acceleration are known requires the quadratic formula, which can produce two mathematically valid solutions. In physical problems, typically only one solution makes physical sense (a positive time value), this calculator’s dual-note flags when this situation arises so you know to check which solution is physically meaningful for your scenario.

Frequently asked questions

Why might solving for time give two different answers?

Because time appears squared in the equation s = ut + ½at², solving for it requires the quadratic formula, which can yield two mathematically valid roots, typically only the positive time value makes physical sense for a real-world scenario.

What’s the difference between this equation and s = ½(u+v)t?

This equation uses acceleration directly (s = ut + ½at²) and doesn’t require knowing the final velocity, while s = ½(u+v)t uses the average of initial and final velocity instead of acceleration, they’re two equivalent ways to describe the same constant-acceleration motion.