Question Video: Determining Whether the Product of Two Quantities is a Scalar or a Vector Quantity Physics • 9th Grade

If an acceleration is multiplied by a time, is the resultant quantity a vector quantity or a scalar quantity?

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Video Transcript

If an acceleration is multiplied by a time, is the resultant quantity a vector quantity or a scalar quantity?

First, we need to recall that a vector quantity has both a magnitude and a direction. An example might be an acceleration of 10 meters per second squared down. Here, we have both the magnitude of 10 meters per second squared and the direction of down. A scalar quantity, on the other hand, has a magnitude only. An example might be a time, say, of two seconds. So, what happens if we multiply these two quantities?

We have our acceleration of 10 meters per second down multiplied by a time of two seconds. First, we multiply the two numbers together, which gives us 10 times two or 20. And then, we take our units of meters per second squared multiplied by seconds, which gives us meters per second and still down. So, we can imagine, say, something starting from rest and then falling with an acceleration of 10 meters per second squared in a downward direction and doing so for two seconds. Its velocity of the two-second mark would be 20 meters per second down. And here, we have both the magnitude of 20 meters per second and the direction of down, making the result a vector.

Therefore, if an acceleration is multiplied by a time, the resultant quantity is a vector quantity.

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