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How to Calculate Resultant Velocity

by Matthew D'Antuono, Demand Media

    Physics can be a challenging course for anyone because it combines science with math and introduces potentially difficult concepts. One basic concept is the concept of speed and how it changes. Calculating the speed of an object can be a simple process if a few basic rules are kept in mind. Learn how to solve problems where you need to find the resultant velocity.

    Acceleration

    Step 1

    Find the acceleration of the object, the time the object is being accelerated and the initial velocity. These values are usually given to you in the problem. If the force is given, find the acceleration by dividing the force on the object by its mass.

    Step 2

    Convert all units to standard units. Acceleration should be in meters per second squared. Velocity should be in meters per second, and time should be in seconds.

    Step 3

    Multiply the acceleration by the time the object is being accelerated. For example, if an object falls for 3 seconds, multiply 3 by 9.8 meters per second squared, which is the acceleration from gravity. The resultant velocity in this case is 29.4 meters per second.

    Step 4

    Add this velocity to the initial velocity. In the example above, if the object had an initial velocity of 5 meters per second, the resultant velocity would be 34.4 meters per second. The overall formula here is v (final) - at + v (initial) where "v" is velocity, "a" is acceleration and "t" is time. In this example the equation would look like this: v (final) = 9.8 x 3 + 5, giving us a result of 34.4.

    After Impact

    Step 1

    Identify the initial velocity of the two objects, the mass of both objects and the final speed of either object if it is given. These values are usually given in the problem.

    Step 2

    Convert all velocities to meters per second and all masses to kilograms.

    Step 3

    Multiply the initial velocity of each object by its mass. Add these two products together to get the total momentum. For example, if both objects have a mass of 5 kilograms, one is at rest and the other is moving at 10 meters per second. The calculation would look like this: 5 x 10 + 5 x 0. This would give us a result of 50 kilogram-meters per second.

    Step 4

    Divide the total momentum by the sum of the masses if the two objects stick together after impact. This will give you the resultant velocity of the two objects. In the example above, we would take 50 and divide by the sum of the masses, which is 10, getting a result of 5 meters per second. If the objects do not stick together, subtract the product of the mass and the final velocity of one object from the total initial momentum. Then, divide the difference by the mass of the other object. This will give you the resultant velocity of the other object. In the example from the previous step, if the final velocity of the object originally moving at 10 meters per second was 2 meters per second, our calculation would look like this: (50 - 10) / 5, which gives us a result of 8 meters per second.

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    Tips

    • Make sure all the units are in standard form before doing any calculations.
    • Write down all the information you need before starting your calculations.
    • Draw a picture of the problem to help you understand what is going on.

    References

    • Physics, 5th Edition; Douglas Giancoli; 2002.

    About the Author

    Matthew D'Antuono is a freelance writer whose work has appeared on websites, such as eHow.com. When he's not writing, he teaches high school physics. D'Antuono earned both a Bachelor of Science in physics and a Bachelor of Arts in philosophy from James Madison University and William Paterson University respectively; he is currently pursuing a master's degree in special education.

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