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How do you find the average velocity in calculus?

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Quick Answer

Average velocity is the result of dividing the distance an object travels by the time it takes to travel that far. The formula for calculating average velocity is therefore: final position - initial position/final time - original time, or [d(1) - d(0)]/[t(1) - t(0)]. Average velocity is expressed as a ratio, such as “miles per hour,” of distance displaced to time in motion.

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How do you find the average velocity in calculus?
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Full Answer

Using the formula for average velocity, it's possible to find the distance displaced by subtracting the object’s final position from its starting position (d(1) - d(0)). Then, a person calculates the time it took to travel from the given points (t(1) - t(2)). It's important to use the data given and plug them into the appropriate slots within the formula for average velocity. The answer needs to be labeled in units of distance traveled over units of time traveled.

The formula for average velocity changes if the object’s velocity alters during travel. When an object changes its velocity at different instances, the average velocity is the sum of velocities at different points divided by the number of points or instances.

The velocity of an object refers to the change in displacement over the change in time. Displacement and velocity are both vector quantities with both direction and magnitude.

The relationship between speed and velocity is similar to the relationship between distance and displacement. Displacement refers to the shortest path between two points. Velocity is therefore distinct from speed because it does not account for the distance traveled but rather for distance displaced in a straight line between two points.

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