How Do You Calculate the Displacement

Physics Displacement Calculator

Calculate the change in position using kinematics

Calculation Result:

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How Do You Calculate Displacement?

In physics, displacement is defined as the change in position of an object. Unlike distance, which is a scalar quantity measuring the total path traveled, displacement is a vector quantity, meaning it has both magnitude and direction.

The Basic Displacement Formula

The simplest way to calculate displacement is when you know the starting and ending points on a straight line:

Δx = x_final – x_initial

Kinematic Displacement Formula

When an object is moving with a constant acceleration, we use the kinematic equation integrated into the calculator above:

d = (v₀ * t) + (½ * a * t²)

• d: Displacement (meters)
• v₀: Initial velocity (meters per second)
• t: Time elapsed (seconds)
• a: Acceleration (meters per second squared)

Practical Example

Imagine a car starts at a velocity of 10 m/s and accelerates at a rate of 2 m/s² for a duration of 5 seconds. To find the displacement:

1. Initial Velocity (v₀) = 10 m/s
2. Time (t) = 5 s
3. Acceleration (a) = 2 m/s²
4. Calculation: (10 * 5) + (0.5 * 2 * 5²)
5. Result: 50 + (1 * 25) = 75 meters

Difference Between Distance and Displacement

If you walk 10 meters forward and 10 meters backward, your distance is 20 meters, but your displacement is 0 meters because your final position is the same as your starting position.

function calculateDisplacement() { var v0 = document.getElementById('initialVelocity').value; var t = document.getElementById('timeElapsed').value; var a = document.getElementById('accelerationRate').value; var resultDiv = document.getElementById('displacementOutput'); var resultText = document.getElementById('resultText'); var formulaText = document.getElementById('formulaUsed'); if (v0 === "" || t === "" || a === "") { alert("Please fill in all fields to calculate displacement."); return; } var initialV = parseFloat(v0); var timeT = parseFloat(t); var accelA = parseFloat(a); if (isNaN(initialV) || isNaN(timeT) || isNaN(accelA)) { alert("Please enter valid numeric values."); return; } // Formula: d = (v0 * t) + (0.5 * a * t^2) var displacement = (initialV * timeT) + (0.5 * accelA * Math.pow(timeT, 2)); resultText.innerHTML = displacement.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " Meters"; formulaText.innerHTML = "Calculated using: (" + initialV + " * " + timeT + ") + (0.5 * " + accelA + " * " + timeT + "²)"; resultDiv.style.display = 'block'; }