If a speed is multiplied by a time, is the resultant quantity a vector quantity or a scalar quantity?
Okay, so in this question, we’re talking about multiplying firstly a speed, we’ll call the speed 𝑠, by a time. And we’ll call this time 𝑡. And what we’re trying to find out here is whether the resultant quantity, speed times time, is a vector quantity or a scalar quantity. So let’s first start by recalling that a scalar quantity is one which only has a magnitude or size, whereas a vector quantity has both a magnitude and direction. So to work out whether the quantity, speed times time, is a vector or a scalar quantity, let’s first think about speed and time individually and whether they are vectors or scalars.
Now, we can recall that speed is defined as a distance moved by, say, an object divided by the time taken for that object to move that distance. And this must mean that speed is not a vector quantity because the distance moved by an object can be in any direction. The direction is not important. And therefore, the quantity distance does not have a direction. It only has a magnitude or size. And the same is true for time. Time does not have any particular spatial direction. And so if neither distance nor time have any information about spatial direction, then the quantity speed also cannot have any information about spatial direction. Therefore, speed only has a magnitude. It’s a scalar quantity.
And so in our quantity here, speed times time, we can label speed as being a scalar. And as we’ve already seen here, time is also a scalar quantity, which means that when we find the quantity, speed times time, we’re multiplying a scalar quantity by a scalar quantity. And neither of the scalars have any information about direction. They have no directionality, which means that the full quantity, speed multiplied by time, also cannot have any directionality.
Therefore, we found the answer to our question. If a speed is multiplied by a time, the resultant quantity is a scalar quantity.