How to Calculate Velocity From Force & Distance

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In physics, you perform work when you apply force to an object and move it over a distance. No work happens if the object does not move, no matter how much force you apply. When you perform work, it generates kinetic energy. The mass and velocity of an object impact how much kinetic energy it has. Equating work and kinetic energy allows you to determine velocity from force and distance. You cannot use force and distance alone, however; since kinetic energy relies on mass, you must determine the mass of the moving object as well.

    Weigh the object on the mass balance. If the balance uses grams, divide the mass by 1,000 to convert to kilograms. If you have a 700 g object, for example, divide by 1,000 to get 0.7 kg.

    Assume friction is negligible in your calculations, so that the work done on the object equals its kinetic energy.

    Set the equations for work and kinetic energy equal to each other. Work equals force times distance and kinetic energy equals one-half the mass of the object times its velocity squared, so F_d = (m_ ÷ _2)_v2.

    Substitute the measurements for force, distance and mass into the equation. If the force is 2 Newtons, the distance is 5 m and the mass is 0.7 kg, for example, (2 N)(5 m) = (0.7 kg ÷ _2)_v2.

    Multiply and divide to simplify the equation. For example, (2 N)(5 m) = (0.7 kg ÷ _2)_v2 becomes 10 N_m = (0.35 kg)_v2.

    Divide the left side of the equation by the number on the right side of the equation to isolate v2. For example, 10 N_m = (0.35 kg)_v2 becomes 28.6 N*m/kg = v2.

    Take the square root of the number on the left side of the equation to find the velocity. For 28.6 N*m/kg = v2, for example, the square root of 28.6 equals 5.3, so the velocity is 5.3 m/s.

    Tips

    • If you do not have a mass balance, weigh the object on a bathroom scale or other scale and multiply the weight by 0.45 to convert pounds to kilograms. For objects too large to weigh, estimate the weight then convert to kilograms.

References

About the Author

Petra Wakefield is a writing professional whose work appears on various websites, focusing primarily on topics about science, fitness and outdoor activities. She holds a Master of Science in agricultural engineering from Texas A&M University.

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