Displacement from Velocity-Time

How it is calculated

The tool uses two constant-acceleration formulas: s = u·t + ½·a·t² for displacement and v = u + a·t for final velocity. The variables are u, the initial velocity in m/s, a, the acceleration in m/s², t, the time in seconds, s, the displacement in metres, and v, the final velocity in m/s. Nothing is converted, so every input must already be in metres and seconds. The sign matters: choose one direction as positive, and a velocity or acceleration pointing the other way is negative. Time cannot be negative, and all three fields are required. Both results are rounded to two decimals.

Common mistakes

• Entering a deceleration as a positive number. Braking from 20 m/s needs a = −4; with a = 4 the tool computes a car that speeds up and returns 78.00 m.
• Reading displacement as distance travelled. With u = 20, a = −4 and t = 8 the result is 32.00 m and −12.00 m/s: the object stopped after 5 s (50.00 m), turned back and ended up closer to the start.
• Applying the formulas past the moment a real object would stop. A braking car does not reverse, so keep t no larger than −u/a, here 5 s.
• Typing km/h or minutes. The formulas only work in m/s, m/s² and seconds, so convert first (72 km/h is 20 m/s).
• Using the tool when acceleration changes during the motion. Both formulas assume a constant a for the whole time.