Content

• Steps
• Method 1 of 2: Calculating Distance by Speed ​​and Time
• Method 2 of 2: Calculating the Distance Between Two Points
• Similar articles

Distance (denoted as d) is the length of a straight line between two points. The distance can be found between two fixed points, and you can find the distance traveled by a moving body. In most cases, the distance can be calculated using the following formulas: d = s × t, where d is distance, s is speed, t is time; d = √ ((x₂ - x₁) + (y₂ - y₁), where (x₁, y₁) and (x₂, y₂) - coordinates of two points.

Steps

Method 1 of 2: Calculating Distance by Speed ​​and Time

1. 1 To calculate the distance traveled by a moving body, you need to know the body's speed and travel time in order to substitute them in the formula d = s × t.
   • Example. The car travels at a speed of 120 km / h for 30 minutes. It is necessary to calculate the distance traveled.
2. 2 Multiply the speed and time and you will find the distance traveled.
   • Pay attention to the units of measurement of the quantities. If they are different, you need to convert one of them to match the other unit. In our example, speed is measured in kilometers per hour and time is measured in minutes. Therefore, it is necessary to convert minutes to hours; for this, the time value in minutes must be divided by 60 and you will get the time value in hours: 30/60 = 0.5 hours.
   • In our example: 120 km / h x 0.5 h = 60 km. Note that the unit of measure "hour" is shortened and the unit of measure "km" (ie distance) remains.
3. 3 The described formula can be used to calculate the values ​​included in it. To do this, isolate the desired value on one side of the formula and substitute the values ​​of the other two quantities into it. For example, to calculate speed, use the formula s = d / t, and to calculate the time - t = d / s.
   • Example. The car drove 60 km in 50 minutes. In this case, its speed is s = d / t = 60/50 = 1.2 km / min.
   • Please note that the result is measured in km / min. To convert this unit to km / h, multiply the result by 60 and get 72 km / h.
4. 4 This formula calculates the average speed, that is, it is assumed that the body has a constant (unchanged) speed throughout the entire travel time. This is suitable for abstract tasks and modeling the movement of bodies. In real life, the speed of a body can change, that is, the body can accelerate, slow down, stop, or move in the opposite direction.
   • In the previous example, we found that a car that traveled 60 km in 50 minutes was traveling at a speed of 72 km / h. This is only true if the vehicle speed has not changed over time. For example, if for 25 minutes (0.42 hours) the car was driving at 80 km / h, and for another 25 minutes (0.42 hours) at 64 km / h, it will also travel 60 km in 50 minutes. (80 x 0.42 + 64 x 0.42 = 60).
   • For problems involving the changing speed of a body, it is better to use derivatives rather than a formula for calculating speed over distance and time.

Method 2 of 2: Calculating the Distance Between Two Points

1. 1 Find two points of spatial coordinates. If you are given two fixed points, then in order to calculate the distance between these points, you need to know their coordinates; in one dimensional space (on the number line) you need the x coordinates₁ and x₂, in two-dimensional space - coordinates (x₁, y₁) and (x₂, y₂), in three-dimensional space - coordinates (x₁, y₁, z₁) and (x₂, y₂, z₂).
2. 2 Calculate the distance in one-dimensional space (the points lie on one horizontal line) using the formula:d = | x₂ - x₁|, that is, you subtract the "x" coordinates and then find the modulus of the resulting value.
   • Notice the modulus (absolute value) brackets are included in the formula. The modulus of a number is the non-negative value of that number (that is, the modulus of a negative number is equal to this number with a plus sign).
   • Example. The car is located between two cities. The city in front of it is 5 km away, and the city behind it is 1 km away. Calculate the distance between cities. If we take the car as a reference point (for 0), then the coordinate of the first city x₁ = 5, and the second x₂ = -1. Distance between cities:
     • d = | x₂ - x₁|
     • = |-1 - 5|
     • = |-6| = 6 km.
3. 3 Calculate the distance in two-dimensional space using the formula:d = √ ((x₂ - x₁) + (y₂ - y₁))... That is, you subtract the "x" coordinates, subtract the "y" coordinates, square the resulting values, add the squares, and then extract the square root from the resulting value.
   • The formula for calculating distance in two-dimensional space is based on the Pythagorean theorem, which states that the hypotenuse of a right triangle is equal to the square root of the sum of the squares of both legs.
   • Example. Find the distance between two points with coordinates (3, -10) and (11, 7) (center of the circle and a point on the circle, respectively).
   • d = √ ((x₂ - x₁) + (y₂ - y₁))
   • d = √ ((11 - 3) + (7 - -10))
   • d = √ (64 + 289)
   • d = √ (353) = 18,79
4. 4 Calculate the distance in 3D space using the formula:d = √ ((x₂ - x₁) + (y₂ - y₁) + (z₂ - z₁))... This formula is a modified formula for calculating distance in two-dimensional space with the addition of a third “z” coordinate.
   • Example. An astronaut is in outer space near two asteroids. The first of them is located 8 kilometers in front of the cosmonaut, 2 km to the right of him and 5 km below him; the second asteroid is 3 km behind the astronaut, 3 km to the left of him, and 4 km above him. Thus, the coordinates of the asteroids are (8.2, -5) and (-3, -3.4). The distance between asteroids is calculated as follows:
   • d = √ ((- 3 - 8) + (-3 - 2) + (4 - -5))
   • d = √ ((- 11) + (-5) + (9))
   • d = √ (121 + 25 + 81)
   • d = √ (227) = 15.07 km

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