How to Calculate Speed & Distance

You can calculate speed and distance using the straightforward definitions for those objects. The distance and speed formulas involve dividing distance by time to calculate the speed of an object.

If you measured how long it took for an object to travel a certain distance, you could divide the distance the object traveled by how long it took to travel to get the speed. If you measure the speed of an object that travels in a specific direction, that's the velocity. Because velocity is how fast an object travels in a direction, velocity is a vector.

Calculating how long it takes for you to run a mile tells you the average speed over the mile, but not the speed at every given moment during the run. Instead, you can determine a small interval over which to measure speed to get the speed at a single moment during the run, which is exactly how speedometers tell you the current speed of your car. Don't get the speeds mixed up.

If you want to get a speed as close as possible to the instantaneous speed of an object, you need to make the interval of time as small as possible. This would mean measuring how fast an object moves in as small as a fraction of a second.

Speedometers

Speedometers in cars work by using a shaft in which a needle moves around a circular dial. A magnet exerts an attractive force on a metallic drum. With greater speeds, the magnetic force becomes greater, which causes the needle to give a speed reading.

Similar to the equations for speed with a given distance and time, the speedometer in a car can give a more precise speed with a smaller time interval. However, the speed it gives must be spread over a reasonable distance and time so that it can adjust with the acceleration and deceleration of a car accordingly. Engineers who manufacture cars ensure the speedometer readings are accurate with respect to the instantaneous speed of a car.

Speed and Density

For a liquid that falls to the ground, you can calculate the weight of the object using its density and volume. From there, if you know the velocity of the object, you can calculate its momentum. You can also calculate specific gravity, a ratio of the density of a substance to the density of a reference substance.

The specific gravity, SG, relates to the two densities with the equation SG = ρsubstance / ρreference with "rho" ρ as the density for the substance and the reference. The units for each density must match each other as a ratio of mass to volume. For this reason, kg/m3 is often used as units for density. Water is usually used as a reference.

You can also calculate weight using specific gravity and volume. If you know the specific gravity of a substance, you can determine its density. Multiply the density by volume to get the substance's mass. Use the equation W = mg to convert mass to weight using the weight W in newtons, mass m in kilograms and gravitational acceleration constant g as 9.8 m/s2.

Conversion Tables

The Engineering Toolbox provides charts for the specific gravity of water at various temperatures and pressures. You can use it to determine the density of a substance with respect to water.

You can use a density conversion table to compare the density of a substance to a density of a reference. Then, you can determine the mass of the substance by multiplying the density by volume. Multiplying the mass by velocity gives you the momentum of the substance.

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About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.