Displacement Calculator

Understanding Displacement Calculator

Displacement under uniform acceleration combines the distance from constant velocity (v₀t) and the additional distance from acceleration (½at²).

How to use this calculator

1. Enter the initial velocity, \(v_0\), in units like \(\text{m/s}\).
2. Enter the acceleration, \(a\), in units like \(\text{m/s}^2\).
3. Enter the time, \(t\), in seconds.
4. Click calculate to get the displacement, \(s\), and follow the step-by-step result.

The formula explained

The formula \(s = v_0 t + \frac{1}{2}at^2\) computes displacement for motion with constant acceleration. It combines the distance from the starting velocity and the extra distance added by acceleration.

• s = displacement
• \(v_0\) = initial velocity
• a = acceleration
• t = time

Step by step method

1. Multiply the initial velocity \(v_0\) by time \(t\).
2. Square the time \(t\), then multiply by acceleration \(a\), then multiply by \(\frac{1}{2}\).
3. Add the two parts together to get \(s\).

Worked example

Problem. A car starts with an initial velocity of \(8\,\text{m/s}\), accelerates at \(2\,\text{m/s}^2\), and moves for \(5\,\text{s}\). Find the displacement.

1. Use \(s = v_0 t + \frac{1}{2}at^2\).
2. Substitute the values: \(s = 8(5) + \frac{1}{2}(2)(5^2)\). This gives \(s = 40 + 25\).
3. Add the parts: \(s = 65\,\text{m}\).

Tips and common mistakes

• Make sure time is in seconds, because the formula assumes \(t\) is measured that way.
• Displacement can be negative if the motion is in the opposite direction, so watch the signs on \(v_0\) and \(a\).

Frequently asked questions