How to Calculate Magnitude of Average Acceleration

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Learn to calculate the magnitude of average acceleration to find the rate of change of an object's velocity. Acceleration has units of length per square second. Like all vector quantities, average acceleration has a magnitude and direction found by manipulating its "x" and "y" components. For example, an average acceleration might be written as 20 feet per square second in the "x" direction and 10 feet per square second in the "y" direction. Finding the magnitude of the average acceleration tells you the size of the acceleration.

Things You'll Need

  • Calculator
  • Square the "x" component of the average acceleration. Call the result "A." Achieve the squaring of a number by multiplying it by itself once. For example, given an "x" component of 20 feet per square second, the result is 20 feet per square second times 20 feet per square second, or 400 square feet per second^4 for "A." The symbol "^" denotes an exponent and is read as "to the power."

  • Square the "y" component of the average acceleration. Call the result "B." Assume the "y" component is 10 feet per square second, for the example. You have 10 feet per square second times 10 feet per square second, or 100 square feet per second^4 for "B."

  • Add the quantities "A" and "B" and call the result "C." Performing this step, for the example, leads to 400 square feet per second^4 plus 100 square feet per second^4, or 500 square feet per second^4 for "C."

  • Compute the square root of "C" to obtain the magnitude of the average acceleration. Use the "Square root" button on a calculator. Completing this exercise leads to the square root of 500 square feet per second^4, which equals an average acceleration magnitude of 22.4 feet per square second. Note that the square root of the unit's square feet per second^4 equals feet per square second.

Tips & Warnings

  • Horizontal vector components are termed "x," while vertical vector components are labelled "y."

References

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