How to Find a Distance From Velocity & Time
Velocity is the change in position (x), or distance, over time. If you know the change in position and the amount of time taken to complete the journey, you can determine velocity. Similarly, if you have any two of these variables, you can always solve for the third.
The relationship between these three variables is as follows:
How to Find Velocity
A car drives from Baltimore to Washington, D.C. in 1.5 hours. If you know that it’s 38 miles between the two cities, what was the car’s average velocity during the trip? Since, this is a trip that goes in one direction, the change in position is the same as distance. Since you know time and the distance, you can solve for velocity by plugging in the distance formula in physics:
So you know your answer is 25.3, but this isn’t quite complete: 25.3 what? Units are just as important as the numerical answer when it comes to physics problems, so don’t lose track of what you’re using to measure distance and time. Since you’re measuring distance in miles and time in hours, your final answer is miles divided by hours, or miles per hour.
Try another example:
A bicyclist completes a 550 meter race in 1.5 hours. What is the bike’s velocity in meters per second? Here, since you need to determine the velocity in meters per second, first convert time to seconds:
(1.5hours)(60minutes)(60seconds)=5,400seconds
Then, plug your known variables into the velocity formula:
Distance Formula in Physics
If you know how fast and how long something was traveling, you can solve for the distance traveled. You just need to rearrange the velocity formula above to get the distance formula in physics:
△x=(velocity)(time)
A plane travels 150 miles per hour on it’s way from Atlanta to San Diego. How far has the plane traveled in 3.5 hours?
Since the plane appears to be going in one direction (toward San Diego) in a straight line, you can assume that the change in position equals distance. Plug your known variables into the distance formula:{\bigtriangleup x} =(150mph)(3.5h) = 525 miles
△x=(150mph)(3.5h)=525miles
Make sure to pay attention to units when using the distance formula in physics. If you’re using a velocity that’s miles per hour, and you’re solving for distance, make sure your time is in hours too.
Solving for Time
If you need to solve for time, you just rearrange the formula one more time:
Say a turtle crawls at 3 mph. How long will it take the turtle to finish a 5-mile race?
Speed Versus Velocity
People tend to use “speed” for “velocity” and vice versa, but they are slightly different concepts. Speed doesn’t take into account direction, while velocity does. If you look at the formula, velocity is the change in position over time, while speed is distance over time. Let’s look at an example to illustrate:
Say you drive 20 miles from your house to your college campus and then head back. It took you an hour round trip. What is your average speed?
You know your total distance and the time taken, so plug into the formula for speed:
Now, what is your average velocity? Keep in mind that you use change in location or displacement to determine velocity because direction matters:
Since you end at your beginning location, your change in position or distance is actually 0, which means your velocity is also 0. Velocity is equal to the formula for speed only if you’re traveling in a straight line.
How to Calculate Time and Distance from Acceleration and Velocity
In a physics equation, given a constant acceleration and the change in velocity of an object, you can figure out both the time involved and the distance traveled. For instance, imagine you’re a drag racer. Your acceleration is 26.6 meters per second2, and your final speed is 146.3 meters per second. Now find the total distance traveled. Got you, huh? “Not at all,” you say, supremely confident. “Just let me get my calculator.”
You know the acceleration and the final speed, and you want to know the total distance required to get to that speed. This problem looks like a puzzler, but if you need the time, you can always solve for it. You know the final speed, vf,and the initial speed, vi (which is zero), and you know the acceleration, a. Because vf – vi = at, you know that
In other words, the total distance traveled is 402 meters, or a quarter mile. Must be a quarter-mile racetrack.
Distance Speed Time Formula
Speed is a measure of how quickly an object moves from one place to another. It is equal to the distance traveled divided by the time. It is possible to find any of these three values using the other two. This picture is helpful:
The positions of the words in the triangle show where they need to go in the equations. To find the speed, distance is over time in the triangle, so speed is distance divided by time. To find distance, speed is beside time, so distance is speed multiplied by time.
s = speed (meters/second)
d = distance traveled (meters)
t = time (seconds)
Distance Speed Time Formula Questions:
1) A dog runs from one side of a park to the other. The park is 80.0 meters across. The dog takes 16.0 seconds to cross the park. What is the speed of the dog?
Answer: The distance the dog travels and the time it takes are given. The dog’s speed can be found with the formula:
s = 5.0 m/s
The speed of the dog is 5.0 meters per second.
2) A golf cart is driven at its top speed of 27.0 km/h for 10.0 minutes. In meters, how far did the golf cart travel?
Answer: The first step to solve this problem is to change the units of the speed and time so that the answer found will be in meters, since this is what the question asks for. The speed is:
s = 27.0 km/h
s = 7.50 m/s
Converting the units, the speed is 7.50 m/s. The time the cart traveled for was:
t = 10.0 min
t = 600sThe speed of the cart and the time of travel are given, so the distance traveled can be found using the formula:
d = st
d = (7.50 m/s)(600 s)
d = 4500 m
The golf cart traveled 4500 m, which is equal to 4.50 km.
Velocity Calculator
This velocity calculator is a comprehensive tool that enables you to estimate the speed of an object. If you have ever wondered how to find velocity, here you can do it in three different ways. The first one relies on the basic velocity definition that uses the well-known velocity equation. The second method calculates what is velocity change caused by acceleration over a specific time interval. Finally, the third part of the velocity calculator makes use of the average velocity formula, which may be useful if you need to analyze journeys with various velocities over different distances.
We’ve also prepared a brief but informative article about velocity itself. Keep reading to learn what is velocity formula and what are the most common velocity units. Did you know that there is an essential difference between speed vs velocity? We’ve written about it from the point of view of a physicist in the text below.
What is velocity? – velocity definition
Velocity definition states that it is the rate of change of the object’s position as a function of time. It is one of the fundamental concepts in classical mechanics that considers the motion of bodies. If you want to put this rule down in the form of a mathematical formula, the velocity equation will be as follows:
velocity = distance / time
Keep in mind that this velocity formula only works when an object has a constant speed in a constant direction or if you want to find average velocity over a certain distance (as opposed to the instantaneous velocity). You have probably noticed that we use words speed and velocity interchangeably, but you can’t do it every time. To learn more about it, head to the speed vs velocity section.
Aside from the linear velocity, to which we devoted this calculator, there are also other types of velocity, such as rotational or angular velocity with corresponding physical quantities: rotational kinetic energy, angular acceleration or mass moment of inertia. When an object has only angular velocity, it doesn’t displace (the distance is zero), and you can’t use the average velocity formula.
The average velocity formula and velocity units
The average velocity formula describes the relationship between the length of your route and the time it takes to travel. For example, if you drive a car for a distance of 70 miles in one hour, your average velocity equals 70 mph. In the previous section, we have introduced the basic velocity equation, but as you probably have already realized, there are more equations in the velocity calculator. Let’s list and organize them below:
- Simple velocity equation:
velocity = distance / time
- Velocity after a certain time of acceleration:
final velocity = initial velocity + acceleration * time
- Average velocity formula – weighted average of velocities:
average velocity = velocity₁ * time₁ + velocity₂ * time₂ + ...
You should use the average velocity formula if you can divide your route into few segments. For example, you drive a car with a speed of 25 mph for 1 h in the city and then reach 70 mph for 3 h on the highway. What is your average velocity? With the velocity calculator, you can find that it will be about 59 mph.
From the above equations, you can also imagine what are velocity units. British imperial units are feet per second ft/s and miles per hour mph. In the metric SI system the units are meters per second m/s and kilometers per hour km/h. Remember you can always easily switch between all of them in our tool!
The relationship between distance and time is also needed when estimating the fuel use of your car. In order to calculate how much gas will be used during a particular journey, try our gas calculator .
How to calculate velocity – speed vs velocity
Before we explain how to calculate velocity, we’d like to note that there is a slight difference between velocity and speed. The former is determined on the difference between the final and initial position and the direction of movement, while the latter requires only the distance covered. In other words, velocity is a vector (with the magnitude and direction), and speed is a scalar (with magnitude only).
It’s time to use the average velocity formula in practice. Provided an object traveled 500 meters in 3 minutes, to calculate the average velocity you should take the following steps:
- Change minutes into seconds (so that the final result would be in meters per second).
3 minutes = 3 * 60 = 180 seconds, - Divide the distance by time:
velocity = 500 / 180 = 2.77 m/s.
Let’s try another example. You want to participate in a race with your brand new car that can change its speed with an acceleration of about 6.95 m/s². The competition just started. What will be your velocity after 4 seconds?
- Set initial velocity to zero, you’re not moving at the beginning of the race.
- Multiply the acceleration by time to obtain the velocity change:
velocity change = 6.95 * 4 = 27.8 m/s. - Since the initial velocity was zero, the final velocity is equal to the change of speed.
- You can convert units to
km/hby multiplying the result by 3.6:27.8 * 3.6 ≈ 100 km/h.
You can, of course, make your calculations much easier by using the average velocity calculator. All you’ll need to do is type in distance and time. One of the advantages of using this calculator is that you don’t have to convert any units by hand. Our tool will do it all for you!
Remember that you can’t race everywhere, normal roads and highways are not built for super high speeds! Check out the car crash calculator to see how dangerous automobile collisions can be. Be sure to not drive after drinking alcohol and inspect your car regularly.
Terminal velocity, escape velocity and relativistic velocity
Velocity is present in many aspects of physics, and we have created many calculators about it! The first velocity is the so-called terminal velocity, which is the highest velocity attainable by a free falling object. Terminal velocity occurs in fluids (e.g., air or water) and depends on the fluid’s density. You can read more about it in our free fall with air resistance calculator.
Knowing how to calculate velocity is of particular importance in astrophysics since results have to be very accurate. If you’re interested in the world of massive celestial objects like suns or planets, visit our escape velocity calculator or orbital velocity calculator. You can learn a lot there!
In the high energy region, there is another important velocity – relativistic velocity. It results from the fact that no object with a non-zero mass can reach the speed of light. Why? When it approaches light speed, it’s kinetic energy becomes unattainable, very large or even infinite. You can check it with the relativistic kinetic energy calculator by filling the velocity field with the speed of light 299,792,458 m/s or 2.998e8 m/s in scientific notation. Moreover, this is a cause of other phenomena like relativistic velocity addition, time dilation, and length contraction. Also the Albert Einstein’s famous E = mc2 formula bases on the relativistic velocity concept.
I hope we’ve convinced you that velocity plays an essential role in everyday life and not just science, and we hope that you’ve enjoyed our velocity calculator. Feel free to explore our other calculators. It may be surprising, but there are many more of them connected with velocity that we didn’t mention, have an explore!
FAQ
What is the airspeed velocity of an unladen swallow?
Well, that depends if you are talking about the European or African variety. For the European sort, it would seem to be roughly 11 m/s, or 24 mph. If it’s our African avian acquaintance you’re after, well i’m afraid your out of luck, the juries still out.
How do you find instantaneous velocity?
- Find an equation that describes how distance (x) changes with respect to time (t).
- Differentiate the formula with respect to time.
- Let dx/dt = instantaneous velocity.
- Input the desired time into the differentiated formula. The result is the instantaneous speed at time t.
How long does it take to reach terminal velocity?
It will take the average human approximately 15 seconds to reach 99% of terminal velocity with their belly facing the Earth. Reach 100% terminal velocity is very difficult, if not impossible, as acceleration drops exponentially as an object approaches its terminal velocity. This time will change if the person’s changes body position.
Can velocity be negative?
Yes, velocity can be negative. Velocity is directional speed, so if the object is moving opposite to the direction defined as the positive direction, it will be negative. Two objects with equal but opposite velocities have the same speed, but are just moving in opposite directions.
How do you find initial velocity?
- Work out which of the displacement (S), final velocity (V), acceleration (A) and time (T) you have to solve for initial velocity (U).
- If you have V, A and T, use U = V – AT.
- If you have S, V and T, use U = 2(S/T) – V.
- If you have S, V and A, use U = SQRT(V2 – 2AS).
- If you have S, A and T, use U = (S/T) – (AT/2).
How do you find final velocity?
- Work out which of the displacement (S), initial velocity (U), acceleration (A) and time (T) you have to solve for final velocity (V).
- If you have U, A and T, use V = U + AT.
- If you have S, U and T, use V = 2(S/T) – U.
- If you have S, A and T, use V = (S/T) + (AT/2).
What is escape velocity?
Escape velocity is the minimum speed an object needs to escape another objects gravitational pull. The most common example of this is the speed a spacecraft requires to leave Earth for distant planets, which is approximately 11.2 km/s.
What is the difference between velocity and acceleration?
Velocity is the speed and direction with which an object is moving, while acceleration is how the speed of that object changes with time. The units for velocity are m/s, while for acceleration they are m/s2.
What causes a change in velocity?
Interactions with other objects cause velocity to change. When a moving object collides with another object in its path, it will slow down (if it collides with something smaller, e.g. an air particle) or stop (if it hits a wall). If an object expels matter behind it, it will speed up, like a rocket. An object will also accelerate towards other objects via gravity.
How do I calculate escape velocity?
- Find the object’s mass in kilograms, M, and its radius in meters, R.
- Multiply M by the gravitational constant (6.674 x 10-11) and then by 2.
- Divide the result of step 2 by R.
- Raise the result of step 3 by 0.5. The result is the escape velocity.
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