Enter any three inputs and click on Calculate button
How to use this Displacement Calculator 🤔
There are input fields for Initial Velocity \((u)\), Acceleration \((a)\), Time \((t)\), and Displacement \((d)\). Enter any three inputs and click on Calculate button.
The calculator uses the \( s = u \cdot t + \frac{ a \cdot t ^2}{2} \) formula, substitues given values, and calcuates the missing value(s).
A missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
What is Displacement?
Displacement is the overall change in position of an object. It tells us how far and in what direction an object has moved from its starting point. Unlike distance, displacement considers the direction of motion, making it a vector quantity.
Calculating Displacement
Displacement (s) can be calculated using the formula:
\( s = u \cdot t + \frac{1}{2} a \cdot t^2 \).
In this formula, the parameters are defined as follows:
u: The initial velocity, or the speed at which the object starts moving.
t: The time duration for which the object has been moving.
a: The acceleration, or the rate at which the object’s speed is changing.
Input and Output Combinations of the Displacement Calculator
Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.
Calculator InputsSet #1
u Initial Velocity
a Acceleration
t Time
For these given inputs,
Outputs, Formulas
We calculate the following outputs:
Displacement\(d = \)\( u \cdot t + \frac{ a \cdot t ^2}{2} \)
{
"topic": "displacement",
"input_types": [
"float",
"float",
"float",
"float"
],
"input_labels": [
"u",
"a",
"t",
"d"
],
"input_descriptions": [
"Initial Velocity",
"Acceleration",
"Time",
"Displacement"
],
"input_units": [
"m/s",
"m/s<sup>2</sup>",
"s",
"m"
],
"input_values": [
"",
"",
"",
""
],
"formula_mathjax": "\\( s = u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)",
"input_pre_msg": "Enter any three inputs and click on Calculate button",
"type": "Calculate",
"title": "Displacement Calculator",
"description": "Calculate the displacement of an object with our Displacement Calculator. Input initial position, final position, and time to get accurate results. Perfect for physics students, teachers, and enthusiasts.",
"category": "Kinematics",
"template": "physics",
"formulas": [
{
"parameters": [
"u",
"a",
"t"
],
"outputs": [
{
"label": "d",
"formula": " u * t + ( a * t * t )/2 ",
"formula_mathjax": "\\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)",
"formula_mathjax_sub": "\\( u \\times t + \\frac{ a \\times t ^2}{2} \\)"
}
],
"example_heading": "What is the distance travelled by an object travelling with an initial velocity of _u_, an acceleration of _a_, for _t_ ?",
"examples": [
{
"u": 5,
"a": 2,
"t": 10,
"d": "150"
},
{
"u": 0,
"a": 10,
"t": 20,
"d": "2000"
}
]
},
{
"parameters": [
"d",
"a",
"t"
],
"outputs": [
{
"label": "u",
"formula": " d / t - ( a * t )/2 ",
"formula_mathjax": "\\( \\frac{ d }{ t } - \\frac{ a \\cdot t }{2} \\)",
"formula_mathjax_sub": "\\( \\frac{ d }{ t } - \\frac{ a \\times t }{2} \\)"
}
],
"example_heading": "What is the initial velocity of an object that has travelled a distance of _d_ with an acceleration of _a_, for _t_ ?",
"examples": [
{
"d": 100,
"a": 2,
"t": 10,
"u": "0"
}
]
},
{
"parameters": [
"d",
"u",
"t"
],
"outputs": [
{
"label": "a",
"formula": " 2 * ( d - ( u * t ))/( t * t ) ",
"formula_mathjax": "\\( 2 \\cdot (\\frac{ d - u \\cdot t }{ t ^2 }) \\)",
"formula_mathjax_sub": "\\( 2 \\times (\\frac{ d - u \\times t }{ t ^2 }) \\)"
}
],
"example_heading": "What is the acceleration of an object that has travelled a distance of _d_ in _t_ with an initial velocity of _u_ ?",
"examples": [
{
"d": 100,
"u": 25,
"t": 5,
"a": "-2"
}
]
}
],
"content": "<h2>What is Displacement?</h2><p>Displacement is the overall change in position of an object. It tells us how far and in what direction an object has moved from its starting point. Unlike distance, displacement considers the direction of motion, making it a vector quantity.</p><h2>Calculating Displacement</h2><p>Displacement (<strong>s</strong>) can be calculated using the formula:</p><p class=\"formula_highlite\">\\( s = u \\cdot t + \\frac{1}{2} a \\cdot t^2 \\).</p><p>In this formula, the parameters are defined as follows:</p><ul><li><strong>u</strong>: The initial velocity, or the speed at which the object starts moving.</li><li><strong>t</strong>: The time duration for which the object has been moving.</li><li><strong>a</strong>: The acceleration, or the rate at which the object’s speed is changing.</li></ul><br><h2>Input and Output Combinations of the Displacement Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">u</span> Initial Velocity</li><li><span class=\"input\">a</span> Acceleration</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Displacement</span><span class=\"output\">\\(d = \\)\\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">d</span> Displacement</li><li><span class=\"input\">a</span> Acceleration</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial Velocity</span><span class=\"output\">\\(u = \\)\\( \\frac{ d }{ t } - \\frac{ a \\cdot t }{2} \\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div><div class=\"formula_set set_3\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #3</span><ul class=\"given\"><li><span class=\"input\">d</span> Displacement</li><li><span class=\"input\">u</span> Initial Velocity</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Acceleration</span><span class=\"output\">\\(a = \\)\\( 2 \\cdot (\\frac{ d - u \\cdot t }{ t ^2 }) \\)</span></li></ul><a class=\"button\" href=\"#example_4\">1 Example</a></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n What is the distance travelled by an object travelling with an initial velocity of <strong>5 m/s</strong>, an acceleration of <strong>2 m/s<sup>2</sup></strong>, for <strong>10 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Initial Velocity, u = 5 m/s</li><li>Acceleration, a = 2 m/s<sup>2</sup></li><li>Time, t = 10 s</li></ul>\n <p>Calculating displacement (d)...</p><p class=\"step\">\\( d = \\) \\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</p><p class=\"step\">\\( d = \\) \\(5\\times10+ \\frac{2\\times10^2}{2} \\)</p><p class=\"step answer\">\\( d = \\) 150 m</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n What is the distance travelled by an object travelling with an initial velocity of <strong>0 m/s</strong>, an acceleration of <strong>10 m/s<sup>2</sup></strong>, for <strong>20 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Initial Velocity, u = 0 m/s</li><li>Acceleration, a = 10 m/s<sup>2</sup></li><li>Time, t = 20 s</li></ul>\n <p>Calculating displacement (d)...</p><p class=\"step\">\\( d = \\) \\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</p><p class=\"step\">\\( d = \\) \\(0\\times20+ \\frac{10\\times20^2}{2} \\)</p><p class=\"step answer\">\\( d = \\) 2000 m</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n What is the initial velocity of an object that has travelled a distance of <strong>100 m</strong> with an acceleration of <strong>2 m/s<sup>2</sup></strong>, for <strong>10 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Displacement, d = 100 m</li><li>Acceleration, a = 2 m/s<sup>2</sup></li><li>Time, t = 10 s</li></ul>\n <p>Calculating initial velocity (u)...</p><p class=\"step\">\\( u = \\) \\( \\frac{ d }{ t } - \\frac{ a \\cdot t }{2} \\)</p><p class=\"step\">\\( u = \\) \\( \\frac{100}{10} - \\frac{2\\times10}{2} \\)</p><p class=\"step answer\">\\( u = \\) 0 m/s</p>\n </div>\n \n <div id=\"example_4\" class=\"example\">\n <span class=\"example_n\">4</span>\n <h3 class=\"question\">\n What is the acceleration of an object that has travelled a distance of <strong>100 m</strong> in <strong>5 s</strong> with an initial velocity of <strong>25 m/s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Displacement, d = 100 m</li><li>Initial Velocity, u = 25 m/s</li><li>Time, t = 5 s</li></ul>\n <p>Calculating acceleration (a)...</p><p class=\"step\">\\( a = \\) \\( 2 \\cdot (\\frac{ d - u \\cdot t }{ t ^2 }) \\)</p><p class=\"step\">\\( a = \\) \\( 2 \\times (\\frac{100-25\\times5}{5^2 }) \\)</p><p class=\"step answer\">\\( a = \\) -2 m/s<sup>2</sup></p>\n </div>\n <br><h2>Input and Output Combinations of the Displacement Calculator</h2><p>Here are the input combinations available for the calculator, along with the formulas it uses to calculate the corresponding outputs.</p><div class=\"formula_sets\"><div class=\"formula_set set_1\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #1</span><ul class=\"given\"><li><span class=\"input\">u</span> Initial Velocity</li><li><span class=\"input\">a</span> Acceleration</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Displacement</span><span class=\"output\">\\(d = \\)\\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</span></li></ul><a class=\"button\" href=\"#example_1\">2 Examples</a></div><div class=\"formula_set set_2\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #2</span><ul class=\"given\"><li><span class=\"input\">d</span> Displacement</li><li><span class=\"input\">a</span> Acceleration</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Initial Velocity</span><span class=\"output\">\\(u = \\)\\( \\frac{ d }{ t } - \\frac{ a \\cdot t }{2} \\)</span></li></ul><a class=\"button\" href=\"#example_3\">1 Example</a></div><div class=\"formula_set set_3\"><span class=\"heading_side\">Calculator Inputs</span><span class=\"set_n\">Set #3</span><ul class=\"given\"><li><span class=\"input\">d</span> Displacement</li><li><span class=\"input\">u</span> Initial Velocity</li><li><span class=\"input\">t</span> Time</li></ul><p>For these given inputs,</p><span class=\"heading_side\">Outputs, Formulas</span><p>We calculate the following outputs:</p><ul class=\"find\"><li><span class=\"output_label\">Acceleration</span><span class=\"output\">\\(a = \\)\\( 2 \\cdot (\\frac{ d - u \\cdot t }{ t ^2 }) \\)</span></li></ul><a class=\"button\" href=\"#example_4\">1 Example</a></div></div><br><br><h2>Examples</h2>\n <div id=\"example_1\" class=\"example\">\n <span class=\"example_n\">1</span>\n <h3 class=\"question\">\n What is the distance travelled by an object travelling with an initial velocity of <strong>5 m/s</strong>, an acceleration of <strong>2 m/s<sup>2</sup></strong>, for <strong>10 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Initial Velocity, u = 5 m/s</li><li>Acceleration, a = 2 m/s<sup>2</sup></li><li>Time, t = 10 s</li></ul>\n <p>Calculating displacement (d)...</p><p class=\"step\">\\( d = \\) \\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</p><p class=\"step\">\\( d = \\) \\(5\\times10+ \\frac{2\\times10^2}{2} \\)</p><p class=\"step answer\">\\( d = \\) 150 m</p>\n </div>\n \n <div id=\"example_2\" class=\"example\">\n <span class=\"example_n\">2</span>\n <h3 class=\"question\">\n What is the distance travelled by an object travelling with an initial velocity of <strong>0 m/s</strong>, an acceleration of <strong>10 m/s<sup>2</sup></strong>, for <strong>20 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Initial Velocity, u = 0 m/s</li><li>Acceleration, a = 10 m/s<sup>2</sup></li><li>Time, t = 20 s</li></ul>\n <p>Calculating displacement (d)...</p><p class=\"step\">\\( d = \\) \\( u \\cdot t + \\frac{ a \\cdot t ^2}{2} \\)</p><p class=\"step\">\\( d = \\) \\(0\\times20+ \\frac{10\\times20^2}{2} \\)</p><p class=\"step answer\">\\( d = \\) 2000 m</p>\n </div>\n \n <div id=\"example_3\" class=\"example\">\n <span class=\"example_n\">3</span>\n <h3 class=\"question\">\n What is the initial velocity of an object that has travelled a distance of <strong>100 m</strong> with an acceleration of <strong>2 m/s<sup>2</sup></strong>, for <strong>10 s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Displacement, d = 100 m</li><li>Acceleration, a = 2 m/s<sup>2</sup></li><li>Time, t = 10 s</li></ul>\n <p>Calculating initial velocity (u)...</p><p class=\"step\">\\( u = \\) \\( \\frac{ d }{ t } - \\frac{ a \\cdot t }{2} \\)</p><p class=\"step\">\\( u = \\) \\( \\frac{100}{10} - \\frac{2\\times10}{2} \\)</p><p class=\"step answer\">\\( u = \\) 0 m/s</p>\n </div>\n \n <div id=\"example_4\" class=\"example\">\n <span class=\"example_n\">4</span>\n <h3 class=\"question\">\n What is the acceleration of an object that has travelled a distance of <strong>100 m</strong> in <strong>5 s</strong> with an initial velocity of <strong>25 m/s</strong> ?\n </h3>\n <h4 class=\"answer\">Answer</h4>\n <p>Given:</p>\n <ul><li>Displacement, d = 100 m</li><li>Initial Velocity, u = 25 m/s</li><li>Time, t = 5 s</li></ul>\n <p>Calculating acceleration (a)...</p><p class=\"step\">\\( a = \\) \\( 2 \\cdot (\\frac{ d - u \\cdot t }{ t ^2 }) \\)</p><p class=\"step\">\\( a = \\) \\( 2 \\times (\\frac{100-25\\times5}{5^2 }) \\)</p><p class=\"step answer\">\\( a = \\) -2 m/s<sup>2</sup></p>\n </div>\n "
}
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