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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 23,936 times.
Velocity is a function of time and is determined by the magnitude and direction of motion. [1] X Source of Research Usually in physics problems, you have to calculate the initial velocity (speed and direction of motion) of an object as it begins to move. There are many equations that can be used to calculate the initial velocity. With the information provided in the problem, you can determine the equation to use and easily find the answer.
Steps
Find initial velocity from final velocity, acceleration and time [2] X Research Source
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Determine the correct equation to use. To solve any physics problem, you must know which equation to use. Writing down all the known information is the first step to finding the right equation. If you already have the final velocity, acceleration, and travel time, use the following equation:
- Initial Velocity: V i = V f – (a * t)
- Understand symbols in formulas.
- Vi is “initial velocity”
- V f is “final velocity”
- a is “acceleration”
- t is “time”
- Note: this is the standard equation used when finding the initial velocity.
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Substitute known information into the formula. After writing down all the known information and determining the equation to use, you can substitute values for the variables. It is important that you write down each step carefully.
- If there is an error, you can easily detect it by reviewing all the previous steps.
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Solve the equation. After replacing all known data, you solve the problem in the correct order of calculations. If allowed, you should use a handheld computer to limit simple errors.
- Example: An object moves east with an acceleration of 10 m/s 2 , and it takes 12 seconds to reach a final velocity of 200 m/s. Find the initial velocity of the object.
- Write down the information you know:
- V i = ?, V f = 200 m/s, a = 10 m/s 2 , t = 12 s
- Multiply acceleration by time. a * t = 10 * 12 = 120
- Subtract the final velocity from this product. Vi = V f – (a * t) = 200 – 120 = 80 V i = 80 m/s to the east.
- Write the correct answer. Add the unit of measure, usually in meters per second m/s , and the direction of motion of the object. If the problem doesn’t provide a direction of motion, you can only calculate the speed, not the velocity.
Find initial velocity from distance, time and acceleration [3] X Research Source
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Determine the correct equation to use. To solve any physics problem, you must know which equation to use. Writing down all the known information is the first step to finding the right equation. If you know the distance covered, time, and acceleration of the object, use the following equation:
- Initial Velocity: V i = (d / t) – [(a * t) / 2]
- Understand symbols in formulas.
- Vi is “initial velocity”
- d is “distance”
- a is “acceleration”
- t is “time”
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/f/f0/Find-Initial-Velocity-Step-5-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-5-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/f/f0/Find-Initial-Velocity-Step-5-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-5-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Substitute known information into the formula. After writing down all the known information and determining the equation to use, you can substitute values for the variables. It is important that you write down each step carefully.
- If there is an error, you can easily detect it by reviewing all the previous steps.
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/2/2a/Find-Initial-Velocity-Step-6-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-6-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/2/2a/Find-Initial-Velocity-Step-6-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-6-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Solve the equation. After replacing all known data, you solve the problem in the correct order of calculations. If allowed, you should use a handheld computer to limit simple errors.
- Example: An object moves west with an acceleration of 7 m/s 2 and travels a distance of 150 m in 30 seconds. Find the initial velocity of the object.
- Write down the information you know:
- Vi = ?, d = 150 m, a = 7 m/s 2 , t = 30 s
- Multiply acceleration by time. a * t = 7 * 30 = 210
- Divide the product by two. (a * t) / 2 = 210 / 2 = 105
- Divide distance by time. d / t = 150 / 30 = 5
- Subtract the second quotient from the first quotient. Vi = (d / t) – [(a * t) / 2] = 5 – 105 = -100 V i = -100 m/s to the west.
- Write the correct answer. Add the unit of measure, usually in meters per second m/s , and the direction of motion of the object. If the problem doesn’t provide a direction of motion, you can only calculate the speed, not the velocity.
Find Initial Velocity From Final Velocity, Acceleration and Distance [4] X Research Source
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Determine the correct equation to use. To solve any physics problem, you must know which equation to use. Writing down all the known information is the first step to finding the right equation. If you already have the final velocity, acceleration, and distance covered, use the following equation:
- Initial Velocity: V i = [V f2 – (2 * a * d)]
- Understand symbols in formulas.
- Vi is “initial velocity”
- V f is “final velocity”
- a is “acceleration”
- d is “distance”
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/8/86/Find-Initial-Velocity-Step-8-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-8-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/8/86/Find-Initial-Velocity-Step-8-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-8-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Replace the known information. After writing down all the known information and determining the equation to use, you can substitute values for the variables. It is important that you write down each step carefully.
- If there is an error, you can easily detect it by reviewing all the previous steps.
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/5/5e/Find-Initial-Velocity-Step-9-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-9-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/5/5e/Find-Initial-Velocity-Step-9-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-9-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Solve the equation. After replacing all known data, you solve the problem in the correct order of calculations. If allowed, you should use a handheld computer to limit simple errors.
- Example: An object moving north with an acceleration of 5 m/s 2 , has traveled a distance of 10 m, and reaches a final speed of 12 m/s. Calculate the initial velocity of the object.
- Write down the information you know:
- V i = ?, V f = 12 m/s, a = 5 m/s 2 , d = 10 m
- Calculate the square of the final velocity. V f2 = 12 2 = 144
- Multiply the acceleration by the distance and multiply by two. 2 * a * d = 2 * 5 * 10 = 100
- Subtract this product from the square of the final velocity. V f2 – (2 * a * d) = 144 – 100 = 44
- Calculate the square root of this result. = √ [V f2 – (2 * a * d)] = √44 = 6.633 V i = 6.633 m/s to the north.
- Write the correct answer. Add the unit of measure, usually in meters per second m/s , and the direction of motion of the object. If the problem doesn’t provide a direction of motion, you can only calculate the speed, not the velocity.
Find initial velocity from final velocity, time and distance [5] X Research Source
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Determine the correct equation to use. To solve any physics problem, you must know which equation to use. Writing down all the known information is the first step to finding the right equation. If you already have your final velocity, time, and distance covered, use the following equation:
- Initial velocity: V i = 2(d/t) – V f
- Understand symbols in formulas.
- Vi is “initial velocity”
- V f is “final velocity”
- t is “time”
- d is “distance”
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/f/f5/Find-Initial-Velocity-Step-11-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-11-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/f/f5/Find-Initial-Velocity-Step-11-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-11-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Substitute known information into the formula. After writing down all the known information and determining the equation to use, you can substitute values for the variables. It is important that you write down each step carefully.
- If there is an error, you can easily detect it by reviewing all the previous steps.
{“smallUrl”:”https://www.wikihow.com/images_en/thumb/7/75/Find-Initial-Velocity-Step-12-Version-3.jpg/v4-728px-Find-Initial-Velocity- Step-12-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/7/75/Find-Initial-Velocity-Step-12-Version-3.jpg/ v4-728px-Find-Initial-Velocity-Step-12-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,”bigWidth”:728,”bigHeight”:546,”licensing”:” <div class=”mw-parser-output”></div>”}
Solve the equation. After replacing all known data, you solve the problem in the correct order of calculations. If allowed, you should use a handheld computer to limit simple errors.
- Solve the equation. After replacing all known data, you solve the problem in the correct order of calculations. If allowed, you should use a handheld computer to limit simple errors.
- Write down the information you know:
- V i = ?, V f = 3 m/s, t = 15 s, d = 45 m
- Divide distance by time. (d/t) = (45/15) = 3
- Multiply that value by 2. 2 (d/t) = 2 (45/15) = 6
- Subtract this product from the final velocity. 2(d/t) – V f = 6 – 3 = 3 V i = 3 m/s to the south.
- Write the correct answer. Add the unit of measure, usually in meters per second m/s , and the direction of motion of the object. If the problem doesn’t provide a direction of motion, you can only calculate the speed, not the velocity.
Things you need
- Pencil
- Paper
- Handheld computer (optional)
X
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 23,936 times.
Velocity is a function of time and is determined by the magnitude and direction of motion. [1] X Source of Research Usually in physics problems, you have to calculate the initial velocity (speed and direction of motion) of an object as it begins to move. There are many equations that can be used to calculate the initial velocity. With the information provided in the problem, you can determine the equation to use and easily find the answer.
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