Sometimes solutions aren’t obvious. If you wanted to know how far away an object was from you, you might think, “grab a ruler, a yardstick, a tape measure, anything that can measure distance.” Sure, those will work, but what if you didn’t have those tools at your disposal? This situation is where the distance equation in physics comes in handy!
Distance formula physics problems prove that with a few pieces of information, you can solve an unknown. Now, you might think, “yeah, but when am I ever going to need to know distance without a measuring tool?” Well, pretty much any job that requires you to use physics constantly, like:
- Astronomer
- Geophysicist
- Optician
- Engineer
- Patent attorney
- Programmer
- Scientist
- Project Manager
The human brain is incredibly plastic, meaning it can understand new concepts if you give it the opportunity. After a while, your brain won’t need a measuring tool to get extraordinarily close to the right answer. If you learn how to calculate distance in physics, it will come in handy daily in any of the above jobs.
Can You Give Examples of Distance Formula Physics Problems?
Absolutely! We’ll show you how to calculate distance with velocity and time. These three fundamental concepts are intertwined and can’t exist without each other. You probably already understand these concepts, but we’ll give them some definitions before getting into some distance formula science problems.
- Distance: How far two objects are from each other
- Velocity: The speed an object is traveling
- Time: The seconds, minutes, hours, etc. needed for your calculation
Now that we have some working definitions let’s get into how to calculate distance in physics.
Since we’re looking for distance, let’s start there. The distance equation looks like this:
Velocity×Time=Distance
So if you know an object’s velocity and how long it’s been traveling, you can use these known attributes to find out the distance it’s traveled.
Perhaps you want to know how far a pitcher is from a batter on a baseball diamond. You could get a measuring tool such as a long tape measure and stroll onto the field to find the distance. Or, you could take some measurements you could calculate from your living room just by watching the game.
If you’ve been stuck inside during the pandemic, why not turn some watching time into learning time?
First, we need to know how fast the ball is traveling. This velocity isn’t too hard to figure out because the speed of the pitch is put up on the screen.
In our make-believe game in this distance formula physics problem, let’s say we just watched the pitcher throw the ball at a nice, even 100 miles per hour, or 100mph. Great! We have our speed. But how do we figure out the time?
Let’s say we have a super-accurate stopwatch. We would determine that the pitch took 375 milliseconds or 375ms. Both numbers have to use the same unit, so we’ll calculate with hours in this case. Let’s convert milliseconds to hours by dividing 375 by 1,000 to take us from milliseconds to seconds:
375÷1,000=.375 seconds
Then divide .375 by 60 for minutes:
375,000 seconds÷60=.00625 minutes
Divide by 60 again for hours:
.00625 minutes÷60=0.00010416666 hours
That’s not much time! For comparison, a human eyeblink is in the range of 300 to 400 milliseconds and is about four times faster than the fastest guitar strumming possible. Don’t worry; the numbers are about to get a lot easier to follow. Plug the figures into our formula:
100mph×0.00010416666 hours=0.01041666666 miles
Let’s change that to feet by multiplying by 5,280:
0.01041666666 miles×5,280=55 feet
Now we know that it’s 55 feet from the mound to home plate.
Let’s say we’re calculating how far a car has traveled on its journey. We don’t know the distance, but we know the velocity and how long it’s been traveling. Let’s say the velocity is 50 kilometers per hour or 50kph. It’s been traveling for 2 hours. Now, we need to plug these figures into our distance formula physics problem:
50kph×2hrs=100 kilometers
Now you know how to find distance in physics!
What About Other Units of Velocity, Time, and Distance?
Good point; it’s rarely that cut and dry. If you’re involved in science, you’ll need to know both English and Metric measurements. Let’s say we’re looking for the distance traveled of two objects, but we’re given different measurements of each.
In our first example, we used miles per hour for the baseball, but then kilometers for the car. They both used hours for the time, but let’s change it up. What if we had to compare the distance traveled for another vehicle, but the measurements for that car were given to us in miles for distance and seconds for time?
Again, our first car in the distance equation physics problem traveled 100 kilometers. Our second car traveled at 100 miles per hour (mph) for 900 seconds.
We have another problem because our time and speed are not in the same units. We’ll have to convert one of them so the equation will make sense.
Because mph is a common measurement of car speed, let’s change the time to hours as we did with the baseball earlier. First, we’ll divide 900 by 60 to get minutes:
900÷60=15 minutes
Then divide 15 by 60 to get hours:
15÷60=.25 hours (¼ hours)
Nine hundred seconds is the same as a quarter-hour. Now we can find the distance!
100mph×0.25hours=25 miles.
Excellent, the distance formula science problem is over, right? Not quite, because we still have to compare 100 kilometers to 25 miles. We know that:
1 kilometer=0.621371 miles
Let’s convert our miles to kilometers and kilometers to miles. The way we’ll do this is to multiply our 100 kilometers distance by 0.621371:
100 kilometers×0.621371=62.137 miles
And divide our 25 miles by 0.621371:
25 miles÷0.621371=40.233 kilometers
Now that we have both figures translated, whether we’re using English or Metric measurements, we can compare the distances these fictional cars traveled in our distance equation physics problems.
What Else Can We Calculate in Physics?
Remember earlier when we said that distance, velocity, and time were all linked together? It’s true! When you know any two of these measurements, you can find the others, too.
And while it’s great to have computer skills, sometimes you need to already have such concepts in your head. To find velocity and time, we will go about distance formula physics equations from other directions.
Finding Velocity
If you know your distance and your time, but not velocity, there’s an equation to help you out:
Distance÷Time=Velocity
Let’s turn back to our fictional cars from previous distance equations. If we know our car has traveled 25 miles and did so in 15 minutes, or .25 hours, we can set up the equation like this:
25 miles÷.25 hours=Velocity
25 miles÷.25 hours=100 miles.
It works! Let’s try it for our metric car, too:
100 kilometers÷2 hours= 50kph
Works like a charm. The same rules about having equivalent measurements throughout the formula apply here, as well.
Finding Time
Let’s say we know how fast the car is going and how far it’s going, but we don’t know how long it will take. Like the distance formula physics problems from before, as long as we know two measurements, we can find the third. You might not be able to keep time, but you don’t need rhythm to find time. The time formula goes as follows:
Distance÷Velocity=Time
This one may be the easiest to find because the methodology is right in the name of our speed, 100 miles per hour. So we know that every hour the car from our distance equation physics problem travels 100 miles. Let’s grab the figures from our problem and plug them in:
25 miles÷100mph=.25 hours
And the same works for our metric car:
100 kilometers÷50kph=2 hours
How to calculate distance in physics can also be demonstrated visually.
The Pyramid
Distance
÷ ÷
Time × Velocity
Take a look at the pyramid above. Distance is on top because if you want to find one of the other two measurements, you always want to divide the distance by them. Distance divided by time is velocity, distance divided by velocity is time.
Take a look at the pyramid above. Distance is on top because if you want to find one of the other two measurements, you always want to divide the distance by them. Distance divided by time is velocity, distance divided by velocity is time.
Time and velocity are multiplied to find distance. You can cover up one of the measurements and find the other. Let’s plug the car information in:
25 miles
÷ ÷
¼ hours × 100mph
You can see their relationship in the pyramid. Multiply ¼ hours by 100mph to get 25 miles. Divide 25 miles by ¼ hours to get 100mph. Divide 25 miles by 100mph to get ¼ hours.
Physics: How To Understand the World
There’s so much more to learn about physics and math, and finding a teacher who can help you understand large concepts can put you on a path toward becoming an engineer, a scientist, or an inventor.
Understanding physics gives you an insight into how the forces that govern the universe work with each other, and something as simple as learning how to calculate distance with velocity and time is the beginning of that understanding.
Now, math can be tough; no one denies that! But the more you apply it to physical problems that can be more easily thought through, the more these lofty ideas will become concrete.
Practice, apply the lessons to real-world questions and watch your brain begin to take hold of these principles and transform the way you perceive your environment. Are there any examples you’ve learned that help you understand physics in a new way? We’d love to hear them! Put them in the comments below and share them with us.
Phina Pipia