SUVAT Equation: Displacement (initial velocity and time) Calculator

Formula first

Overview

This equation represents the area under a velocity-time graph, where the 'ut' term accounts for the rectangular area of initial velocity and the '0.5at²' term accounts for the triangular area resulting from acceleration. It is a fundamental kinematic relation that assumes the acceleration remains uniform throughout the entire duration of motion.

Symbols

Variables

s = Displacement, u = Initial Velocity, a = Acceleration, t = Time

Apply it well

When To Use

When to use: Use this formula when you know the initial velocity, constant acceleration, and the time elapsed, but do not know the final velocity.

Why it matters: It is essential for predicting the exact position of moving objects, such as vehicles braking to a stop or projectiles in flight, which is critical in engineering and transport safety.

Avoid these traps

Common Mistakes

• Forgetting to square the time variable (t²).
• Confusing displacement (s) with total distance traveled if the object changes direction.
• Applying this to situations where acceleration is not constant.

One free problem

Practice Problem

A cyclist starts from rest and accelerates at 2 m/s² for 5 seconds. How far has the cyclist traveled?

Solve for: $s$

Hint: Since the cyclist starts from rest, u = 0, so the equation simplifies to s = 0.5 * a * $t^2$.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Young and Freedman, University Physics with Modern Physics
2. A-Level Physics: Edexcel/AQA Specification Guides
3. AQA Physics Specification (7408) / OCR Physics A (H556)