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Calculating average velocity is a fundamental concept in physics and mathematics that allows us to quantify the rate at which an object changes its position over a specific time period. While velocity refers to the rate of displacement of an object, average velocity takes into account the total distance traveled and the time taken to cover that distance. By understanding how to calculate average velocity, we can better analyze and describe the motion of objects and systems, providing valuable insights into their behavior and characteristics. In this guide, we will explore the steps and formulas involved in determining average velocity, as well as discuss its significance in various real-life scenarios.
This article was co-written by Sean Alexander, MS. Sean Alexander is a math and physics tutor. Sean is the owner of Alexander Tutoring, a private tutoring center that offers personalized sessions with a focus on math and physics. With over 15 years of experience, Sean has tutored physics and math at Stanford University, San Francisco State University and Stanbridge Institute. He holds a bachelor’s degree in physics from the University of California, Santa Barbara, and a master’s degree in theoretical physics from San Francisco State University.
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All you need to calculate average velocity is the total distance traveled, or change in position, and the total time. Remember that velocity determines both the direction of motion and speed, so the answer must state the direction of motion, such as “north”, “forward” or “left”. If the problem has constant acceleration, you can learn to take shortcuts to find an easier solution.
Steps
Calculate average velocity from distance traveled and time
- Directed quantities are called vector quantities . [1] X Research Source They are distinguished from scalar quantities by the arrow mark on the variable. For example, v represents speed, while v → represents velocity (including speed and direction of motion). [2] X Research Source The v used in this article is velocity.
- For science problems, you use meters or another metric unit of distance, but in everyday life you can use any unit you like.
- Assume a rocket flies north for 5 minutes at a constant speed of 120 meters/min. To calculate the final position, we use the formula s = vt, or intuitively know that the rocket will be located (5 minutes) (120 meters/minute) = 600 meters north .
- For problems with constant acceleration, you can solve using the equation s = vt + ½at 2 , or refer to another section for a shorter solution.
- Even in a science problem, if the problem uses hours or longer time units, it may be easier to calculate velocity, then convert your answer to meters/second.
- Remember to write the direction of movement (like “front” or “north”).
- As a formula we have v av = Δs/Δt . The black notation ta Δ indicates “degree of change”, so Δs/Δt is “change of position in degrees of change in time”.
- The average velocity is written as v av , or written as v with the dashed line above it.
- Lan walks west at 1m/s for 2 seconds, then suddenly increases to 3m/s and continues walking west for 2 seconds. Her total teleportation distance is (1m/s west)(2 s) + (3m/s west)(2 s) = 8 meters west. Total travel time is 2s + 2s = 4s. Her average velocity is 8m west / 4s = 2m/s west .
- Dung walks west at 5m/s for 3 seconds, then turns back and goes east at 7m/s for 1 second. We can think of eastward motion as “negative motion”, so total displacement = (5m/s west)(3s) + (-7m/s west) = 8 meters. Total time = 4s. Average velocity = 8 m west / 4s = 2 m/s west .
- Ngoc goes 1 meter north, then 8 meters west, then 1 meter south. The time it takes her to cover this distance is 4 seconds. Draw a diagram on the page, you will see that she has traveled 8 meters west of the original position, so this is her teleport distance. Total travel time is 4s, so average velocity is still 8m west / 4s = 2m/s west .
Calculate average velocity from constant acceleration
- If you don’t understand “m/s 2 “, write it as “m/s/s” or “meter/second/second”. [3] X Research Source Acceleration of 2m/s/s means that every second the velocity increases by 2m/s.
- At the initial moment ( t = 0 s), the bicycle is moving to the right with a speed of 5 m/s.
- After 1 second ( t = 1), the bicycle is running at 5m/s + at = 5m/s + (2 m/s 2 )(1 s) = 7m/s.
- At t = 2, the bicycle moves to the right with a speed of 5+(2)(2) = 9m/s.
- At t = 3, the bicycle moves to the right with a speed of 5+(2)(3) = 11m/s.
- At t = 4, the bicycle moves to the right with a speed of 5+(2)(4) = 13m/s.
- At t = 5, the bicycle moves to the right with a speed of 5+(2)(5) = 15m/s.
- Remember to write the direction of motion, in this case “right”.
- These terms can be alternatively written as v 0 (velocity at time 0 or initial velocity, and v (final velocity).
- Regardless of which pair of numbers we choose, the average of the 2 velocities at those times will always be the same. For example, ((5+15)/2), ((7+13)/2), or ((9+11)/2), all equal 10m/s to the right.
- Since any of these pairs of numbers have the same mean, the average of all these velocities will equal that value. With the example above, the average of all velocities is still 10m/s on the right.
- We can find this value by averaging any pair of numbers, for example initial and final velocities. That is the velocity at times t=0 and t=5, and can be calculated using the above formula: (5+15)/2 = 10m/s on the right.
- s = v i t + ½at 2 . (In theory it should be written as Δs and Δt, or change of position and change of time, but it is also understood if you use s and t.)
- The average velocity v av is defined as s/t, so write the formula in terms of s/t.
- v av = s/t = v i + at
- Acceleration x time is the total change in velocity, or v f – vi i . So we can replace “at” in that formula and get:
- v av = v i + ½(v f – v i ).
- Simplifying the equation we have: v av = v i + ½v f – ½v i = ½v i + ½v f = (v f + v i )/2 .
Advice
- Velocity is different from speed because velocity is a vector quantity, and speed is a scalar quantity. Vector quantities represent both direction and magnitude, while scalar quantities represent magnitude only.
- If the object moves in only one direction, such as left-right, you can use a positive value to indicate one direction (such as right) and a negative value to indicate the other direction (left). Write this rule at the top of the page so your reader understands your problem.
- To calculate the velocity of an object at a particular point in its path, you need to calculate the instantaneous velocity instead of the average velocity.
This article was co-written by Sean Alexander, MS. Sean Alexander is a math and physics tutor. Sean is the owner of Alexander Tutoring, a private tutoring center that offers personalized sessions with a focus on math and physics. With over 15 years of experience, Sean has tutored physics and math at Stanford University, San Francisco State University and Stanbridge Institute. He holds a bachelor’s degree in physics from the University of California, Santa Barbara, and a master’s degree in theoretical physics from San Francisco State University.
This article has been viewed 27,451 times.
All you need to calculate average velocity is the total distance traveled, or change in position, and the total time. Remember that velocity determines both the direction of motion and speed, so the answer must state the direction of motion, such as “north”, “forward” or “left”. If the problem has constant acceleration, you can learn to take shortcuts to find an easier solution.
In conclusion, calculating average velocity is a relatively straightforward process that requires determining the distance traveled and the time taken. By dividing the distance by the time, one can find the average velocity. However, it is important to keep in mind that average velocity only provides information on the overall rate of displacement and does not consider the actual path taken. Additionally, it is crucial to use consistent units for both distance and time when calculating average velocity. Overall, understanding how to calculate average velocity is essential for analyzing an object’s motion and determining its average speed over a given time period.
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