How to Calculate Distance and Speed

Calculating the distance between two points does not require sophisticated math skills. Don’t worry, you only need the basics such as addition, subtraction, multiplication, division, and square numbers. The key is finding the distance between the two points.

And once you know the distance between two points, you can then calculate the speed. You will need even fewer math skills than listed above to find the speed at which an object is traveling between the two points.

Calculating Distance

Let us begin by defining what we mean when we say two points. To keep matters simple, we are talking about coordinates in a 2D space such as an ordinary flat piece of paper.

We will use the Cartesian coordinate system so that we can easily refer to points along a horizontal x-axis and a vertical y-axis. And we will say that the distance we are measuring is in miles.

Now let us choose our two points. Each point will have two coordinates, one on each axis.
For point one our coordinates will be x1=5, y1=7. Our second point has the coordinates x2-16, y2-25.

We begin by using subtraction to find the difference between coordinates on the same axis. So, x2-x1 is the same as 16-5 or 11. And on the y-axis, y2-y1 is the same as 25-7 or 18.

Now find the squares of 11 and 18. The square of 11 is 121 and the square of 18 is 324.
Next, add together the two results. 121 + 324 = 445.

The final step is to find the square root of the sum 445 which is 21.095.

That means the distance between our two points is 21.095. Let us round that number down to 21 miles.

Here is a recap of the steps we used to calculate the distance:

1. Use subtraction to determine the difference between coordinates on the same axis:
(x2-x1) = (16-5) = 11
(y2-y1) = (25-7) = 18

2. Square your results:
11² = 121
18² = 324

3. Use addition to find the sum of the squares:
121 + 324 = 445

4. Find the square root of the sum:
√445 = 21.095 or 21 miles

Calculating Speed

Now that we have the distance between the two points, we can calculate speed.

Let us suppose an object leaves point 1 at six o’clock and arrives at point 2 at eight o’clock. How fast is it traveling?

The established formula for calculating speed is Speed = Distance / Time.

We know the distance is 21 miles. And we know the time it takes to travel the distance is two hours. So we simply need to plug our data that we discovered into the formula to find the speed.

Our formula now looks like this: Speed = 21 miles/2 hours.

A quick bit of division tells us that Speed = 10.5 miles per hour.

To further understand the concept of speed, let’s delve into its different types. Speed can be categorized into average speed and instantaneous speed. Average speed, as we calculated above, is the total distance traveled divided by the total time taken. It gives us a general idea of how fast an object is moving over a period of time. On the other hand, instantaneous speed refers to the speed of an object at a specific moment in time. This is what speedometers in cars measure. For example, if a car’s speedometer reads 60 miles per hour at a particular moment, that is its instantaneous speed. Understanding these different types of speed can help in various practical situations, from driving to physics experiments.