Video Transcript
If a time is multiplied by a velocity, is the resultant quantity a vector quantity or a scalar quantity?
Let’s first recall that a vector quantity has both a magnitude and a direction. An example might be five meters per second west. Here, we have both the magnitude of five meters per second and the direction of west. A scalar quantity, on the other hand, has a magnitude only. An example of a scalar quantity might be one second. So, we can see that time is a scalar and velocity is a vector. So, what we’re doing here is multiplying a scalar by a vector.
So, what happens if we multiply our time of one second by our velocity of five meters per second west? We might imagine, say, a bicycle traveling at a velocity of five meters per second west and doing so for one second. To multiply these quantities, we just multiply the numbers one and five, and one times five equals five, and then the units meters per second times seconds. So, that cancels out the per second, and we’re left with five meters west.
Here, we have both a magnitude and a direction and so the result is a vector. Therefore, when a time is multiplied by a velocity, the resultant quantity is a vector quantity.
