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Distance calculation is a fundamental concept used in various areas of everyday life, science, and engineering. Whether you want to determine the shortest route to a destination, measure the length of a particular object, or predict the motion of an entity in space, knowing how to calculate distance is crucial. This skill allows us to quantify the separation between two points and comprehend the physical or conceptual extent between them. In this guide, we will explore different methods and formulas to accurately calculate distances in a variety of contexts, helping you develop a solid understanding of this essential mathematical concept.
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The distance, usually denoted d , is the measured length of the line connecting two points. Distance refers to the amount of space between two fixed points (for example, a person’s height is the distance from the soles of the feet to the top of the head), or the space between the current position of a moving object with its starting point. Most distance problems can be solved using the equation d = s avg × t where d is the distance, s avg is the average velocity, and t is the time, or using the equation d = √(( x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 ) , where (x 1 , y 1 ) and (x 2 , y 2 ) are the x and y coordinates of the two points.
Steps
Find the distance given time and average velocity
- To better understand the distance calculation method, consider the following example: suppose we are running on a road at 193 km/h and want to know how far we can travel in half an hour. Using 193 km/h as the average velocity value and 0.5 h as the time value, the next step is to solve the distance problem.
- Note that if the unit of time in velocity is different from the unit of time in motion, you must convert either value to the same unit of time. For example, if we have an average velocity in km/h and a travel time in minutes, then you have to divide the time by 60 to convert it to hours.
- Let’s solve the following problem. 193 km/h × 0.5 hours = 96.5 km . Note that the unit in time value (hour) cancels out with the time unit of average velocity in the denominator (hour) so only the distance unit is km.
- For example, suppose a car has traveled 60 km in 50 minutes, but we do not know the average speed of the car. So we keep the variable s avg fixed in the distance equation to get the equation s avg = d/t, then divide 60 km/50 minutes to find 1.2 km/min.
- Note that the velocity found in the above problem has an uncommon unit (km/min). To get the usual speed of km/h we multiply it by 60 minutes/hour and get 72 km/h .
- For example, in the above problem, we assume that to cover a distance of 60 km in 50 minutes, the car must travel at 72 km/h. This is only true when the car maintains a speed of 72 km / h throughout the journey. However, if we run 80 km/h on half the journey and 64 km/h on the other half, you still get 60 km in 50 minutes, so 72 km/h is not the only result!
- Derivative solutions derived from real-world calculations are a more accurate solution to finding the velocity of real-world objects, because of the fact that the velocity is very variable.
Find the distance between two points
- Note that this formula uses absolute values (symbol ” | | “). Absolute value means that the number in the above notation becomes positive if it was previously negative.
- Suppose we stop the car on a perfectly straight highway. If there is a small town 5 km ahead of us and a town 1 km behind, how far apart are those two towns? If we set the coordinates for town 1 to be x 1 = 5 and town 2 to be x 1 = -1, we get the distance d between the two towns as follows:
- d = |x 2 – x 1 |
- =|-1 – 5|
- =|-6| = 6 km .
- The formula for calculating the distance in a 2D plane uses the Pythagorean theorem, according to which the hypotenuse of a right triangle is equal to the square root of the sum of the squares of the other two sides.
- Suppose we have two points on the xy plane whose coordinates: (3, -10) and (11, 7) correspond to the center of the circle and a point lying on the circle. To find the straight distance between these two points, we solve as follows:
- d = ((x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 )
- d = ((11 – 3) 2 + (7 – -10) 2 )
- d = (64 + 289)
- d = (353) = 18.79
- Suppose you are an astronaut flying through space, close to two celestial bodies. One is 8 km ahead of you, 2 km to the right and 5 km below, the other is 3 km behind you, 3 km to the left and 4 km upwards. The coordinates of the two celestial bodies are as follows (8.2,-5) and (-3,-3.4), the distance between them will be:
- d = ((-3 – 8) 2 + (-3 – 2) 2 + (4 – -5) 2 )
- d = ((-11) 2 + (-5) 2 + (9) 2 )
- d = (121 + 25 + 81)
- d = (227) = 15.07 km
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 14 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 23,023 times.
The distance, usually denoted d , is the measured length of the line connecting two points. Distance refers to the amount of space between two fixed points (for example, a person’s height is the distance from the soles of the feet to the top of the head), or the space between the current position of a moving object with its starting point. Most distance problems can be solved using the equation d = s avg × t where d is the distance, s avg is the average velocity, and t is the time, or using the equation d = √(( x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 ) , where (x 1 , y 1 ) and (x 2 , y 2 ) are the x and y coordinates of the two points.
In conclusion, calculating distance is a fundamental skill that is applicable in various fields such as physics, geography, or even everyday scenarios. By understanding the different formulas and techniques involved in distance calculation, one can accurately determine the length between two or more points. Whether it is using the distance formula in mathematics, measuring the displacement in physics, or utilizing GPS technology in navigation, distance calculation provides us with valuable information for making informed decisions and understanding our surroundings. It is important to note that while the concept of distance may seem simple, it can become more complex depending on the scenario and the tools used for measurement. Therefore, it is essential to carefully consider the relevant factors, select the appropriate method, and apply the appropriate formula to obtain accurate distance calculations. Overall, developing a solid understanding of how to calculate distance is a valuable skill that enables us to navigate and comprehend the world around us.
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