Calculator for Physics

:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–dark-text: #333;
–white: #fff;
}
body {
font-family: ‘Segoe UI’, Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–dark-text);
line-height: 1.6;
margin: 0;
padding: 20px;
}
.loan-calc-container {
max-width: 800px;
margin: 30px auto;
background-color: var(–white);
padding: 30px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
}
h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
margin-bottom: 8px;
font-weight: bold;
color: var(–primary-blue);
}
.input-group input[type=”number”],
.input-group select {
width: 100%;
padding: 12px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box; /* Important for padding and width */
font-size: 1rem;
}
.input-group input[type=”number”]:focus,
.input-group select:focus {
border-color: var(–primary-blue);
outline: none;
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: var(–primary-blue);
color: var(–white);
border: none;
border-radius: 4px;
font-size: 1.1rem;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
margin-top: 30px;
padding: 20px;
background-color: var(–success-green);
color: var(–white);
text-align: center;
border-radius: 4px;
font-size: 1.5rem;
font-weight: bold;
min-height: 60px;
display: flex;
align-items: center;
justify-content: center;
box-shadow: inset 0 0 10px rgba(0, 0, 0, 0.2);
}
.explanation {
margin-top: 40px;
padding: 25px;
background-color: var(–white);
border: 1px solid #e0e0e0;
border-radius: 8px;
}
.explanation h2 {
color: var(–primary-blue);
text-align: left;
margin-bottom: 15px;
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.explanation p, .explanation ul {
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}
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@media (max-width: 600px) {
.loan-calc-container {
padding: 20px;
}
h1 {
font-size: 1.8rem;
}
#result {
font-size: 1.2rem;
}
}

This calculator helps you solve for unknown variables in uniformly accelerated motion (constant acceleration) in one dimension.

Understanding One-Dimensional Kinematics

This calculator is based on the fundamental equations of motion for an object moving in a straight line with constant acceleration. These equations, often called the “suvat” equations (where ‘s’ is displacement, ‘u’ is initial velocity, ‘v’ is final velocity, ‘a’ is acceleration, and ‘t’ is time), are cornerstones of classical mechanics.

The five standard kinematic equations for constant acceleration are:

• v = v₀ + at
• Δx = v₀t + ½at²
• Δx = ½(v₀ + v)t
• v² = v₀² + 2aΔx
• Δx = vt - ½at²

This calculator utilizes a selection of these equations to solve for any one unknown variable, provided at least three other variables are known. The calculator will attempt to use the most direct equation for the requested unknown.

How to Use the Calculator:

1. Enter at least three known values from the list: Initial Velocity (v₀), Final Velocity (v), Acceleration (a), Time (t), or Displacement (Δx).
2. Select which variable you want the calculator to solve for from the “Solve For” dropdown.
3. Click the “Calculate” button.
4. The result will appear in the designated area, with units.

Important Notes:

• Ensure all units are consistent (e.g., meters per second for velocity, meters per second squared for acceleration, seconds for time, meters for displacement).
• This calculator assumes constant acceleration. If acceleration changes during the motion, these equations will not apply.
• If you input conflicting values (e.g., a scenario that is physically impossible based on the equations), the calculator might produce an error or an unexpected result. It’s good practice to check your inputs.

Example Scenario:

Imagine a car starting from rest (v₀ = 0 m/s) and accelerating uniformly at 3 m/s² for 10 seconds. We want to find its final velocity and the distance it traveled.

1. Set Initial Velocity (v₀) to 0.
2. Set Acceleration (a) to 3.
3. Set Time (t) to 10.
4. To find Final Velocity (v): Select “Final Velocity (v)” in “Solve For” and click “Calculate”. The result should be 30 m/s.
5. To find Displacement (Δx): Now, keeping v₀=0, a=3, t=10, and having just calculated v=30, you can solve for displacement. Select “Displacement (Δx)” in “Solve For” and click “Calculate”. The result should be 150 m. (Alternatively, you could have used the displacement input to solve for time or acceleration if those were unknown).

function calculateKinematics() {
var v0 = parseFloat(document.getElementById(“initialVelocity”).value);
var v = parseFloat(document.getElementById(“finalVelocity”).value);
var a = parseFloat(document.getElementById(“acceleration”).value);
var t = parseFloat(document.getElementById(“time”).value);
var deltaX = parseFloat(document.getElementById(“displacement”).value);
var unknown = document.getElementById(“unknown”).value;
var resultDiv = document.getElementById(“result”);

var calculatedValue = NaN;
var resultUnit = “”;
var errorMessage = “”;

// Clear previous results and messages
resultDiv.innerHTML = “”;

// Check if at least 3 values are provided (excluding the one to solve for)
var knownValuesCount = 0;
if (!isNaN(v0)) knownValuesCount++;
if (!isNaN(v)) knownValuesCount++;
if (!isNaN(a)) knownValuesCount++;
if (!isNaN(t)) knownValuesCount++;
if (!isNaN(deltaX)) knownValuesCount++;

// Need at least 3 non-NaN values to solve for one unknown
if (knownValuesCount 2*deltaX/t = v0 + v => v = 2*deltaX/t – v0
calculatedValue = (2 * deltaX / t) – v0;
resultUnit = “m/s”;
} else if (!isNaN(v) && !isNaN(a) && !isNaN(t)) {
// Re-arranging v = v0 + at for v0 gives v0 = v – at. This is not solving for v.
// This case implies v is known, and we are solving for v, which is redundant unless other vars allow verification.
// However, standard practice is to solve for an unknown based on other knowns.
// If v is known, and we select to solve for v, it implies the user might want to check consistency or has redundant info.
// We’ll assume the user intends to calculate v using v0, a, t or v0, a, deltaX etc.
// If v is provided AND selected as unknown, it’s best to use an equation that doesn’t involve the provided v.
// But if the user provides v, and wants to SOLVE for v, the most direct is v=v0+at.
// If v is provided and selected to solve for, and v0,a,t are present, we calculate it.
// If v is provided and selected to solve for, and v0,a,deltaX are present, we calculate it.
// If v is provided and selected to solve for, and v0,t,deltaX are present, we calculate it.
// The logic below prioritizes equations where v is truly unknown.
} else {
errorMessage = “Insufficient known values to calculate Final Velocity (v).”;
}
}

// Solve for Initial Velocity (v0)
else if (unknown === “initialVelocity”) {
if (!isNaN(v) && !isNaN(a) && !isNaN(t)) {
calculatedValue = v – a * t;
resultUnit = “m/s”;
} else if (!isNaN(v) && !isNaN(a) && !isNaN(deltaX)) {
calculatedValue = Math.sqrt(v * v – 2 * a * deltaX);
resultUnit = “m/s”;
} else if (!isNaN(v) && !isNaN(t) && !isNaN(deltaX)) {
// deltaX = 0.5 * (v0 + v) * t => 2*deltaX/t = v0 + v => v0 = 2*deltaX/t – v
calculatedValue = (2 * deltaX / t) – v;
resultUnit = “m/s”;
} else if (!isNaN(a) && !isNaN(t) && !isNaN(deltaX)) {
// deltaX = v0*t + 0.5*a*t^2 => v0*t = deltaX – 0.5*a*t^2 => v0 = (deltaX – 0.5*a*t^2) / t
calculatedValue = (deltaX – 0.5 * a * t * t) / t;
resultUnit = “m/s”;
} else {
errorMessage = “Insufficient known values to calculate Initial Velocity (v₀).”;
}
}

// Solve for Acceleration (a)
else if (unknown === “acceleration”) {
if (!isNaN(v) && !isNaN(v0) && !isNaN(t)) {
calculatedValue = (v – v0) / t;
resultUnit = “m/s²”;
} else if (!isNaN(v) && !isNaN(v0) && !isNaN(deltaX)) {
calculatedValue = (v * v – v0 * v0) / (2 * deltaX);
resultUnit = “m/s²”;
} else if (!isNaN(v) && !isNaN(t) && !isNaN(deltaX)) {
// deltaX = v*t – 0.5*a*t^2 => 0.5*a*t^2 = v*t – deltaX => a = 2*(v*t – deltaX) / t^2
calculatedValue = (2 * (v * t – deltaX)) / (t * t);
resultUnit = “m/s²”;
} else if (!isNaN(v0) && !isNaN(t) && !isNaN(deltaX)) {
// deltaX = v0*t + 0.5*a*t^2 => 0.5*a*t^2 = deltaX – v0*t => a = 2*(deltaX – v0*t) / t^2
calculatedValue = (2 * (deltaX – v0 * t)) / (t * t);
resultUnit = “m/s²”;
} else {
errorMessage = “Insufficient known values to calculate Acceleration (a).”;
}
}

// Solve for Time (t)
else if (unknown === “time”) {
// Solving quadratic for t: 0.5*a*t^2 + v0*t – deltaX = 0
// Using the quadratic formula: t = [-b ± sqrt(b^2 – 4ac)] / 2a
// Here, a_quad = 0.5*a, b_quad = v0, c_quad = -deltaX
if (!isNaN(v) && !isNaN(v0) && !isNaN(a)) {
// v = v0 + at => at = v – v0 => t = (v – v0) / a
calculatedValue = (v – v0) / a;
resultUnit = “s”;
} else if (!isNaN(v0) && !isNaN(deltaX) && !isNaN(a)) {
var a_quad = 0.5 * a;
var b_quad = v0;
var c_quad = -deltaX;
var discriminant = b_quad * b_quad – 4 * a_quad * c_quad;

if (discriminant >= 0) {
var t1 = (-b_quad + Math.sqrt(discriminant)) / (2 * a_quad);
var t2 = (-b_quad – Math.sqrt(discriminant)) / (2 * a_quad);
// Typically, we’re interested in the positive time value
if (t1 >= 0 && t2 = 0 && t1 = 0 && t2 >= 0) calculatedValue = Math.min(t1, t2); // Usually the earlier time
else calculatedValue = NaN; // No non-negative time solution
resultUnit = “s”;
} else {
errorMessage = “No real solution for Time (t) with these values (discriminant is negative).”;
}
} else if (!isNaN(v) && !isNaN(deltaX) && !isNaN(a)) {
// deltaX = v*t – 0.5*a*t^2 => 0.5*a*t^2 – v*t + deltaX = 0
// Here, a_quad = 0.5*a, b_quad = -v, c_quad = deltaX
var a_quad = 0.5 * a;
var b_quad = -v;
var c_quad = deltaX;
var discriminant = b_quad * b_quad – 4 * a_quad * c_quad;

if (discriminant >= 0) {
var t1 = (-b_quad + Math.sqrt(discriminant)) / (2 * a_quad);
var t2 = (-b_quad – Math.sqrt(discriminant)) / (2 * a_quad);
if (t1 >= 0 && t2 = 0 && t1 = 0 && t2 >= 0) calculatedValue = Math.min(t1, t2);
else calculatedValue = NaN;
resultUnit = “s”;
} else {
errorMessage = “No real solution for Time (t) with these values (discriminant is negative).”;
}
} else if (!isNaN(v0) && !isNaN(v) && !isNaN(deltaX)) {
// deltaX = 0.5 * (v0 + v) * t => t = 2*deltaX / (v0 + v)
if (v0 + v !== 0) {
calculatedValue = (2 * deltaX) / (v0 + v);
resultUnit = “s”;
} else {
errorMessage = “Cannot divide by zero (v₀ + v = 0).”;
}
} else {
errorMessage = “Insufficient known values to calculate Time (t).”;
}
}

// Solve for Displacement (deltaX)
else if (unknown === “displacement”) {
if (!isNaN(v0) && !isNaN(t) && !isNaN(a)) {
calculatedValue = v0 * t + 0.5 * a * t * t;
resultUnit = “m”;
} else if (!isNaN(v0) && !isNaN(v) && !isNaN(t)) {
calculatedValue = 0.5 * (v0 + v) * t;
resultUnit = “m”;
} else if (!isNaN(v) && !isNaN(t) && !isNaN(a)) {
calculatedValue = v * t – 0.5 * a * t * t;
resultUnit = “m”;
} else if (!isNaN(v0) && !isNaN(v) && !isNaN(a)) {
calculatedValue = (v * v – v0 * v0) / (2 * a);
resultUnit = “m”;
} else {
errorMessage = “Insufficient known values to calculate Displacement (Δx).”;
}
}
}

// Display result or error message
if (!isNaN(calculatedValue)) {
// Round to a reasonable number of decimal places for physics context
var roundedValue = parseFloat(calculatedValue.toFixed(4));
resultDiv.innerHTML = roundedValue + ” ” + resultUnit;
} else {
resultDiv.innerHTML = errorMessage || “Calculation Error”;
}
}