This article was coauthored by Sean Alexander, MS. Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University.
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Velocity is an object's speed in a particular direction. Mathematically, velocity is often described as the change in position over the change in time.^{[1] X Expert Source Sean Alexander, MSAcademic Tutor Expert Interview. 14 May 2020. }^{[2] X Research source } This fundamental concept shows up in many basic physics problems. Which formula you use depends on what you know about the object, so read carefully to make sure you've chosen the right one.
Quick Formulas
 Average velocity =
 final position initial position
 final time initial time
 Average velocity if acceleration is constant =
 initial velocity final velocity
 Average velocity if acceleration is zero and constant =
 Final velocity =
 a = acceleration t = time
Steps
Method 1
Method 1 of 3:Finding Average Velocity

1Find average velocity when acceleration is constant. If an object is accelerating at a constant rate, the formula for average velocity is simple:^{[3] X Research source }. In this equation is the initial velocity, and is the final velocity. Remember, you can only use this equation if there is no change in acceleration.
 As a quick example, let's say a train accelerates at a constant rate from 30 m/s to 80 m/s. The average velocity of the train during this time is .

2Set up an equation with position and time instead. You can also find the velocity from the object's change in position and time. This works for any problem. Note that, unless the object is moving at a constant velocity, your answer will be the average velocity during the movement, not the specific velocity at a certain time.
 The formula for this problem is , or "final position  initial position divided by final time  initial time." You can also write this as = ^{Δx} / _{Δt}, or "change in position over change in time."
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3Find the distance between the start and end points. When measuring velocity, the only positions that matter are where the object started, and where the object ended up. This, along with which direction the object traveled, tells you the displacement, or change in position.^{[4] X Research source } The path the object took between these two points does not matter.

Example 1: A car traveling due east starts at position x = 5 meters. After 8 seconds, the car is at position x = 41 meters. What was the car's displacement?
 The car was displaced by (41m  5m) = 36 meters east.

Example 2: A diver leaps 1 meter straight up off a diving board, then falls downward for 5 meters before hitting the water. What is the diver's displacement?
 The diver ended up 4 meters below the starting point, so her displacement is 4 meters downward, or 4 meters. (0 + 1  5 = 4). Even though the diver traveled six meters (one up, then five down), what matters is that the end point is four meters below the start point.

Example 1: A car traveling due east starts at position x = 5 meters. After 8 seconds, the car is at position x = 41 meters. What was the car's displacement?

4Calculate the change in time. How long did the object take to reach the end point? Many problems will tell you this directly. If it does not, subtract the start time from the end time to find out.
 Example 1 (cont.): The problem tells us that the car took 8 seconds to go from the start point to the end point, so this is the change in time.
 Example 2 (cont.): If the diver jumped at t = 7 seconds and hits the water at t = 8 seconds, the change in time = 8s  7s = 1 second.

5Divide the total displacement by the total time. In order to find the velocity of the moving object, you will need to divide the change in position by the change in time. Specify the direction moved, and you have the average velocity.
 Example 1 (cont.): The car changed its position by 36 meters over 8 seconds. 4.5 m/s east.
 Example 2 (cont): The diver changed her position by 4 meters over 1 second. 4 m/s. (In one dimension, negative numbers are usually used to mean "down" or "left." You could say "4 m/s downward" instead.)

6Solve problems in two dimensions. Not all word problems involve movement back along one line. If the object turns at some point, you may need to draw a diagram and solve a geometry problem to find the distance.

Example 3: A man jogs for 3 meters east, then make a 90º turn and travels 4 meters north. What is his displacement?
 Draw a diagram and connect the start point and end point with a straight line. This is the hypotenuse of a triangle, so solve for its length of this line using properties of right triangles. In this case, the displacement is 5 meters northeast.
 At some point, your math teacher may require you to find the exact direction traveled (the angle above the horizontal). You can do this by using geometry or by adding vectors.
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Example 3: A man jogs for 3 meters east, then make a 90º turn and travels 4 meters north. What is his displacement?
Method 2
Method 2 of 3:Finding Velocity from Acceleration

1Understand the velocity formula for an accelerating object. Acceleration is the change in velocity. If the acceleration is constant, the velocity continues to change at the same rate.^{[5] X Expert Source Sean Alexander, MSAcademic Tutor Expert Interview. 14 May 2020. }We can describe this by multiplying acceleration and time, and adding the result to the initial velocity:
 , or "final velocity = initial velocity + (acceleration * time)"
 Initial velocity is sometimes written as ("velocity at time 0").

2Multiply the acceleration by the change in time. This will tell you how much the velocity increased (or decreased) over this time period.

Example: A ship sailing north at 2 m/s accelerates north at a rate of 10 m/s^{2}. How much did the ship's velocity increase in the next 5 seconds?
 a = 10 m/s^{2}
 t = 5 s
 (a * t) = (10 m/s^{2} * 5 s) = 50 m/s increase in velocity.

Example: A ship sailing north at 2 m/s accelerates north at a rate of 10 m/s^{2}. How much did the ship's velocity increase in the next 5 seconds?

3Add the initial velocity. Now you know the total change in the velocity. Add this to the initial velocity of the object, and you have your answer.

Example (cont): In this example, how fast is the ship traveling after 5 seconds?

Example (cont): In this example, how fast is the ship traveling after 5 seconds?

4Specify the direction of movement. Unlike speed, velocity always includes the direction of movement. Make sure to include this in your answer.
 In our example, since the ship started going north and did not change direction, its final velocity is 52 m/s north.

5Solve related problems. As long as you know the acceleration, and the velocity at any one point in time, you can use this formula to find the velocity at any other time. Here's an example solving for the initial velocity:
 "A train accelerates at 7 m/s^{2} for 4 seconds, and ends up traveling forward at a velocity of 35 m/s. What was its initial velocity?"

Advertisement  "A train accelerates at 7 m/s^{2} for 4 seconds, and ends up traveling forward at a velocity of 35 m/s. What was its initial velocity?"
Method 3
Method 3 of 3:Circular Velocity

1Learn the formula for circular velocity. Circular velocity refers to the velocity that one object must travel in order to maintain its circular orbit around another object, usually a planet or other gravitating mass.^{[6] X Research source }
 The circular velocity of an object is calculated by dividing the circumference of the circular path by the time period over which the object travels.
 When written as a formula, the equation is:
 v = ^{(2πr)} / _{T}
 Note that 2πr equals the circumference of the circular path.
 r stands for "radius"
 T stands for "time period"

2Multiply the circular radius by 2π. The first stage of the problem is calculating the circumference. To do this, multiply the radius by 2π. If you are calculating this by hand, you can use 3.14 as an approximation for π.
 Example: Find the circular velocity of an object traveling a circular path with a radius of 8 m over a full time interval of 45 seconds.
 r = 8 m
 T = 45 s
 Circumference = 2πr = ~ (2)(3.14)(8 m) = 50.24 m
 Example: Find the circular velocity of an object traveling a circular path with a radius of 8 m over a full time interval of 45 seconds.

3Divide this product by the time period. In order to find the circular velocity of the object in question, you need to divide the calculated circumference by the time period over which the object traveled.
 Example: v = ^{(2πr)} / _{T} = ^{50.24 m} / _{45 s} = 1.12 m/s
 The circular velocity of the object is 1.12 m/s.
Advertisement  Example: v = ^{(2πr)} / _{T} = ^{50.24 m} / _{45 s} = 1.12 m/s
Community Q&A

QuestionWhen do we have deceleration?Benjamin WalkerCommunity AnswerAs the object loses energy passing through a medium. The medium an object is passing through will determine the deceleration.

QuestionHow do I calculate the velocity of something given its time traveled and distance covered?Community AnswerDivide distance traveled by the time taken to get the average speed. Velocity is the term used for speed when the object travels in a uniform direction (i.e. straight line or circle).

QuestionHow does velocity change if the distance decreases and the time increases?Community AnswerVelocity decreases. Think about it: It takes a longer time to cover a shorter distance.

QuestionWhat is the formula for velocity if you aren't given time?Community AnswerVelocity squared=(initial velocity squared) + 2 × ( acceleration due to gravity) × ( distance covered) V×V=u×u + 2as.

QuestionA stone is thrown with an initial velocity of 15 m/s. How do I find the velocity at t=35?Community AnswerTo find the velocity, use the equation: Final velocity = initial velocity + (acceleration due to gravity)(time).

QuestionHow can I solve a problem to find initial speed?Community AnswerRearrange the equation so that Vi (Initial speed) is isolated. Once isolated, just plug in the numbers and solve.

QuestionIf an elevator travels 16 meter down in 25 seconds, and than travels 32 meters up in 50 seconds, what is the average speed per meter?Community AnswerYou have to calculate both averages, and then get the mean between the two (though in this instance, both are the same). 1: 16/25 = 0.64 m/s first speed 2: 32/50 = 0.64 m/s second speed 3: (0.64+0.64)/2 = 0.64 average

QuestionHow do I prove that speed is directly proportional to distance?Community Answervelocity = distance/time. As the distance increases, the velocity also increases.

QuestionHow do I find the time from velocity?Community AnswerYou need the distance first; the distance divided by the velocity is the time.

QuestionA body falls from rest with an acceleration of 10m/s^2. What is the going velocity after 5s? How far has it fallen by then?CabbacheCommunity Answer10m/s^2 means that the velocity of the body increases by 10m/s every second. If that happens for 5 seconds, then the velocity at that time would be 10 x 5 = 50m/s. Use the equation s = at^2/2 to find how much it has fallen. S = 10x5^2/2 = 125 meters.
Tips
 Meters per second (m/s) is the standard scientific unit for velocity.^{[7] X Research source } Make sure your units match by measuring distance in meters (m), time in seconds (s), and acceleration in meters per second per second (m/s^{2}).^{[8] X Expert Source Sean Alexander, MSAcademic Tutor Expert Interview. 14 May 2020. }Thanks!
 Average velocity measures the average velocity an object travels over the full course of its path. Instantaneous velocity measures the velocity of an object at a specific moment along its path.Thanks!
References
 ↑ Sean Alexander, MS. Academic Tutor. Expert Interview. 14 May 2020.
 ↑ https://www.khanacademy.org/science/physics/onedimensionalmotion/displacementvelocitytime/a/whatisvelocity
 ↑ https://www.physicsclassroom.com/class/1DKin/Lesson1/SpeedandVelocity
 ↑ http://www.physicsclassroom.com/Class/1DKin/U1L1c.cfm
 ↑ Sean Alexander, MS. Academic Tutor. Expert Interview. 14 May 2020.
 ↑ http://easycalculation.com/physics/classicalphysics/circularvelocity.php
 ↑ https://physics.info/velocity/
 ↑ Sean Alexander, MS. Academic Tutor. Expert Interview. 14 May 2020.
About This Article
To calculate velocity using acceleration, start by multiplying the acceleration by the change in time. For example, if the acceleration is 10 m/s2 and the change in time is 5 seconds, then there is a 50 m/s increase in velocity. Then, add the initial velocity to the increase in velocity. If the initial velocity was 2 m/s, then the final velocity is 52 m/s. If the initial velocity was 0 m/s, then the final velocity is 50 m/s. Be sure to include any directional notations in your answer. To learn more, such as how to calculate average or circular velocity, keep reading the article!
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