How to Calculate Velocity
How to Calculate Velocity
Three Methods:
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. 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 =vav=xf−xitf−ti{\displaystyle v_{av}={\frac {x_{f}x_{i}}{t_{f}t_{i}}}}
 xf={\displaystyle x_{f}=}final position xi={\displaystyle x_{i}=}initial position
 tf={\displaystyle t_{f}=}final time ti={\displaystyle t_{i}=}initial time
 Average velocity if acceleration is constant =vav=vi+vf2{\displaystyle v_{av}={\frac {v_{i}+v_{f}}{2}}}
 vi={\displaystyle v_{i}=}initial velocity vf={\displaystyle v_{f}=}final velocity
 Average velocity if acceleration is zero and constant = vav=xt{\displaystyle v_{av}={\frac {x}{t}}}
 Final velocity =vf=vi+at{\displaystyle v_{f}=v_{i}+at}
 a = acceleration t = time
Steps
Finding Average Velocity

Find average velocity when acceleration is constant.If an object is accelerating at a constant rate, the formula for average velocity is simple:vav=vi+vf2{\displaystyle v_{av}={\frac {v_{i}+v_{f}}{2}}}. In this equationvi{\displaystyle v_{i}}is the initial velocity, andvf{\displaystyle v_{f}}is the final velocity. Remember, you canonlyuse 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 isvav=xf−xitf−ti{\displaystyle v_{av}={\frac {x_{f}x_{i}}{t_{f}t_{i}}}}, or "final position  initial position divided by final time  initial time." You can also write this as vav{\displaystyle v_{av}}=Δx/Δt, or "change in position over change in time."

Find 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 thedisplacement, orchange in position.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 driver 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?

Calculate 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.

Divide 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.vav=36m8s={\displaystyle v_{av}={\frac {36m}{8s}}=}4.5 m/seast.
 Example 2(cont): The diver changed her position by 4 meters over 1 second.vav=−4m1s={\displaystyle v_{av}={\frac {4m}{1s}}=}4 m/s. (In one dimension, negative numbers are usually used to mean "down" or "left." You could say "4 m/s downward" instead.)

Solve 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.

Example 3:A man jogs for 3 meters east, then make a 90º turn and travels 4 meters north. What is his displacement?
Finding Velocity from Acceleration

Understand 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. We can describe this by multiplying acceleration and time, and adding the result to the initial velocity:
 vf=vi+at{\displaystyle v_{f}=v_{i}+at}, or "final velocity = initial velocity + (acceleration * time)"
 Initial velocityvi{\displaystyle v_{i}}is sometimes written asv0{\displaystyle v_{0}}("velocity at time 0").

Multiply 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/s2. How much did the ship's velocity increase in the next 5 seconds?
 a = 10 m/s2
 t = 5 s
 (a * t) = (10 m/s2* 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/s2. How much did the ship's velocity increase in the next 5 seconds?

Add 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?
 vf=vi+at{\displaystyle v_{f}=v_{i}+at}
 vi=2m/s{\displaystyle v_{i}=2m/s}
 at=50m/s{\displaystyle at=50m/s}
 vf=2m/s+50m/s=52m/s{\displaystyle v_{f}=2m/s+50m/s=52m/s}

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

Specify 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.

Solve 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/s2for 4 seconds, and ends up traveling forward at a velocity of 35 m/s. What was its initial velocity?"

vf=vi+at{\displaystyle v_{f}=v_{i}+at}
35m/s=vi+(7m/s2)(4s){\displaystyle 35m/s=v_{i}+(7m/s^{2})(4s)}
35m/s=vi+28m/s{\displaystyle 35m/s=v_{i}+28m/s}
vi=35m/s−28m/s=7m/s{\displaystyle v_{i}=35m/s28m/s=7m/s}

vf=vi+at{\displaystyle v_{f}=v_{i}+at}
 "A train accelerates at 7 m/s2for 4 seconds, and ends up traveling forward at a velocity of 35 m/s. What was its initial velocity?"
Circular Velocity

Learn 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.
 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.
 rstands for "radius"
 Tstands for "time period"

Multiply 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.

Divide 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.
 Example: v =(2πr)/T=50.24 m/45 s= 1.12 m/s
Community Q&A

QuestionHow do I calculate the velocity of something given its time traveled and distance covered?wikiHow ContributorCommunity 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).Thanks!

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.Thanks!

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

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?wikiHow ContributorCommunity 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 averageThanks!

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

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

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

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

How do I find average speed of travel when I know the distance?

How do I find the velocity of something with just the time and without knowing the distance?

How do you find the time from velocity

Calculate the velocity of the object after 2s?

A stone is released from the top of the tower of height 19.6 meter. Calculate the final velocity of the stone before touching the ground?
Quick Summary
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!
 Meters per second (m/s) is the standard scientific unit for velocity. Make sure your units match by measuring distance in meters (m), time in seconds (s), and acceleration in meters per second per second (m/s2).
 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.
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Video: Calculating average velocity or speed  Onedimensional motion  Physics  Khan Academy
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