Calculator Suite

Displacement Calculator

Calculate displacement, initial velocity, acceleration, or time using s = ut + ½at²

Displacement Problem Setup

Use s = ut + ½at² to solve for displacement, initial velocity, acceleration, or time

Common Scenarios

Projectile Motion

Object thrown upward - how far does it travel?

Elevator Motion

How far does an accelerating elevator travel?

Falling Object

How long to fall a certain distance?

Quick Presets

Earth Gravity (-9.81 m/s²)

Displacement Formulas

Key equations for calculating change in position

Primary Equation

s = ut + \frac{1}{2}at^2

Calculates displacement ( $s$ ) given initial velocity ( $u$ ), time ( $t$ ), and acceleration ( $a$ ).

Alternative (No Time)

v^2 = u^2 + 2as

Useful when you know velocities and acceleration but not the time duration.

Understanding Displacement Calculator

TL;DR

Displacement measures change in position (vector), not total distance traveled. Use this calculator to solve for displacement ( $s$ ), velocity ( $u$ ), time ( $t$ ), or acceleration ( $a$ ).

Distance vs. Displacement

Displacement is a vector, meaning it cares about direction. Distance is a scalar, meaning it only cares about "how much ground was covered."

How to Use This Calculator

Select Goal: Choose which variable you need to find (e.g., "Displacement").
Input Values: Enter the known variables (Initial Velocity, Time, Acceleration).
Check Signs: Use positive numbers for one direction (e.g., Up) and negative for the other (e.g., Down).
Review: Check the step-by-step derivation below the results.

Real-World Example: The "Running Track"

Scenario:

You run exactly one lap around a 400m track and end up where you started.

Analysis:

Distance: 400 meters (total ground covered).
Displacement: $0$ meters (final position - initial position = 0).

3 Key Checks (The "SOP")

Vector Check

Did you end up negative? That just means you are behind where you started.

Sign Check

Gravity pointing down? Make sure $g$ is negative (e.g., -9.81).

Time Check

Time cannot be negative. If you get $t < 0$ , check your inputs.

Assumptions & Limitations

Constant Acceleration: Formula assumes $a$ never changes.
1D Motion: This tool calculates motion along a straight line (1 dimension).
Point Mass: Ignores the object's size and rotation.

Video Tutorials

Distance vs Displacement (Khan Academy)

Position-Time Graphs

Frequently Asked Questions

Can displacement be negative?

Yes! Negative displacement simply means you ended up in the "negative" direction from where you started (e.g., behind the start line, or below the drop point).

What if calculated displacement is 0?

It means the object returned to its exact starting position. It definitely moved, but its net change in position is zero.

Why is it ½at² and not just at²?

This comes from calculus (integration). Visually, on a velocity-time graph, the distance is the area of a triangle, which is $\frac{1}{2} \times \text{base} \times \text{height}$ .

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