mrua calculator - Aaron Graves, PhDude Replica

MRUA Calculator (Uniformly Accelerated Motion)

Use this tool to solve common MRUA scenarios. Enter values using SI units (meters, seconds, m/s, m/s²).

Calculation mode

Initial position, x₀ (m)

Final position, x (m)

Initial velocity, v₀ (m/s)

Final velocity, v (m/s)

Acceleration, a (m/s²)

Time, t (s)

What is MRUA?

MRUA stands for Movimiento Rectilíneo Uniformemente Acelerado, often called uniformly accelerated rectilinear motion in English. It describes motion in a straight line where acceleration remains constant over time.

In practical terms, MRUA appears whenever velocity changes at a fixed rate: a car speeding up on a straight road, a bike braking steadily, or an object moving in one direction under constant net force.

Core Equations Used in This Calculator

1) Velocity as a function of time

v = v₀ + a·t

2) Position as a function of time

x = x₀ + v₀·t + ½·a·t²

3) Displacement and average velocity (constant acceleration)

Δx = x - x₀
v_avg = (v₀ + v) / 2
Δx = v_avg·t

How to Use the MRUA Calculator

Select a calculation mode based on the values you already know.
Enter all required inputs.
Click Calculate to get instant results.
Use Load Example if you want to test the calculator quickly.

Tip: If initial position is not provided in your problem, you can usually set x₀ = 0.

Worked Example

Problem

A runner starts at x₀ = 0 m with initial velocity v₀ = 3 m/s and accelerates at a = 1.5 m/s² for t = 6 s. Find final velocity and final position.

Solution

v = v₀ + a·t = 3 + 1.5·6 = 12 m/s
x = x₀ + v₀·t + ½·a·t² = 0 + 3·6 + 0.5·1.5·36 = 45 m

So after 6 seconds, the runner is moving at 12 m/s and has reached 45 meters.

Common Mistakes to Avoid

Mixing units (e.g., km/h with m/s).
Forgetting signs: deceleration is usually a negative acceleration if positive direction is forward.
Entering time as negative when the problem refers to elapsed time.
Confusing position (x) with displacement (Δx).

Sign Convention Quick Guide

Choose one direction as positive and keep it consistent:

Motion in positive direction: velocity is positive.
Motion in negative direction: velocity is negative.
Acceleration opposing motion often appears with opposite sign.

Why This Matters

MRUA is foundational in physics and engineering. Once you master constant-acceleration motion, you can solve more advanced topics such as projectile motion, dynamics, and control systems with confidence.