How to Calculate Distance

Step-by-Step Guide

1. 1

   Step 1: Find values for average speed and time.

   When you try to find the distance a moving object has traveled, two pieces of information are vital for making this calculation: its speed (or velocity magnitude) and the time that it has been moving.
   
   With this information, it's possible to find the distance the object has traveled using the formula d = savg × t.
   
   To better understand the process of using the distance formula, let's solve an example problem in this section.
   
   Let's say that we're barreling down the road at 120 miles per hour (about 193 km per hour) and we want to know how far we will travel in half an hour.
   
   Using 120 mph as our value for average speed and
   0.5 hours as our value for time, we'll solve this problem in the next step.
2. 2

   Step 2: Multiply average speed by time.

   Once you know the average speed of a moving object and the time it's been traveling, finding the distance it has traveled is relatively straightforward.
   
   Simply multiply these two quantities to find your answer.
   
   Note, however, that if the units of time used in your average speed value are different than those used in your time value, you'll need to convert one or the other so that they are compatible.
   
   For instance, if we have a average speed value that's measured in km per hour and a time value that's measured in minutes, you would need to divide the time value by 60 to convert it to hours.
   
   Let's solve our example problem. 120 miles/hour ×
   0.5 hours = 60 miles.
   
   Note that the units in the time value (hours) cancel with the units in the denominator of the average speed (hours) to leave only distance units (miles). , The simplicity of the basic distance equation (d = savg × t) makes it quite easy to use the equation for finding the values of variables besides distance.
   
   Simply isolate the variable you want to solve for according to the basic rules of algebra, then insert values for your other two variables to find the value for the third.
   
   In other words, to find your object's average speed, use the equation savg = d/t and to find to find the time an object has been traveling, use the equation t = d/savg.
   
   For instance, let's say that we know that a car has driven 60 miles in 50 minutes, but we don't have a value for the average speed while traveling.
   
   In this case, we might isolate the savg variable in the basic distance equation to get savg = d/t, then simply divide 60 miles / 50 minutes to get an answer of
   1.2 miles/minute.
   
   Note that in our example, our answer for speed has an uncommon units (miles/minute).
   
   To get your answer in the more common form of miles/hour, multiply it by 60 minutes/hour to get 72 miles/hour. , It's important to understand that the basic distance formula offers a simplified view of the movement of an object.
   
   The distance formula assumes that the moving object has constant speed — in other words, it assumes that the object in motion is moving at a single, unchanging rate of speed.
   
   For abstract math problems, such as the ones you may encounter in an academic setting, sometimes it's still possible to model an object's motion using this assumption.
   
   In real life, however, this model often doesn't accurately reflect the motion of moving objects, which can, in reality, speed up, slow down, stop, and reverse over time.
   
   For instance, in the example problem above, we concluded that to travel 60 miles in 50 minutes, we'd need to travel at 72 miles/hour.
   
   However, this is only true if travel at one speed for the entire trip.
   
   For instance, by traveling at 80 miles/hr for half of the trip and 64 miles/hour for the other half, we will still travel 60 miles in 50 minutes — 72 miles/hour = 60 miles/50 min = ????? Calculus-based solutions using derivatives are often a better choice than the distance formula for defining an object's speed in real-world situations because changes in speed are likely.
3. 3

   Step 3: Manipulate the equation to solve for other variables.

4. 4

   Step 4: Note that the "savg" variable in the distance formula refers to average speed.

Detailed Guide

About the Author