SUVAT Calculator

Understanding SUVAT Calculator

SUVAT equations describe motion with constant acceleration. S=displacement, U=initial velocity, V=final velocity, A=acceleration, T=time.

How to use this calculator

1. Enter the values you already know, such as initial speed, acceleration, time, or displacement.
2. Choose the missing quantity you want to find.
3. The calculator uses the SUVAT equations to rearrange the known values and compute the answer.
4. Check that your units are consistent, for example metres, seconds, and metres per second.

The formula explained

The formulas \(v = u + at\) and \(s = ut + \frac{1}{2}at^2\) calculate final velocity and displacement for motion with constant acceleration. They work when acceleration does not change during the time interval.

• u = initial velocity, the starting speed with direction
• v = final velocity, the speed after time \(t\)
• a = constant acceleration
• t = time elapsed
• s = displacement, the change in position

Step by step method

1. Start by writing down the values you know and the one you need to find.
2. Pick the SUVAT equation that includes your known values and the unknown, then rearrange it if needed.
3. Substitute the numbers carefully, keeping units consistent, then calculate the result.

Worked example

Problem. A car starts at \(u = 5\,\text{m/s}\) and accelerates at \(a = 2\,\text{m/s}^2\) for \(t = 4\,\text{s}\). Find the final velocity \(v\) and the displacement \(s\).

1. Use \(v = u + at\), so \(v = 5 + (2)(4)\).
2. Calculate \(v = 13\,\text{m/s}\). Then use \(s = ut + \frac{1}{2}at^2\), so \(s = (5)(4) + \frac{1}{2}(2)(4^2)\).
3. Calculate \(s = 20 + 16 = 36\,\text{m}\).

Tips and common mistakes

• Make sure acceleration is constant, because these equations do not apply if acceleration changes.
• Watch the sign of each quantity, especially if motion in one direction is treated as negative.

Frequently asked questions