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Question Video: Defining Velocity in Terms of Displacement and Time Science

Fill in the blank: A velocity is a speed in a particular direction. Velocity is the change of _ with time.

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Video Transcript

Fill in the blank. A velocity is a speed in a particular direction. Velocity is the change of blank with time. (A) Distance, (B) displacement, (C) speed.

This question is asking us to recall the definition of velocity. Let’s look at each of the options given to us.

First, we can rule out option (C). It’s incorrect to say velocity is a change in speed with time. A change in speed with time is actually equal to the quantity of acceleration. So this is not the answer.

Next, let’s consider option (A), the change of distance with time. Recall that this is actually equal to the definition of speed. The question actually tells us that a velocity is a speed in a particular direction. This reminds us that, unlike speed, velocity is a vector quantity. It has to have both magnitude and direction. For example, if we wanted to describe the motion of this person, we could say their speed is three miles per hour. But to describe their velocity, we’d have to say three miles per hour east. Velocity and speed are similar, but they are not the same. So option (A) cannot be the answer.

Next, let’s consider option (B), the change in displacement with time. Displacement is a similar quantity to distance. But it is important to be aware that displacement and distance are not interchangeable. The distance traveled by an object is equal to the length of the path that it took. The displacement of the object is the distance from an object’s starting point to its endpoint in a particular direction. For example, if a person is walking and they changed direction during their journey, their displacement is different to the distance they traveled.

Let’s think about this person who walked from point 𝐴 to point 𝐵 and then changed direction and went to point 𝐶. In this case, the distance traveled is the length of this path. But the displacement is measured between the starting point and the endpoint of the journey. So the distance traveled by the person is greater than the person’s displacement.

It is also important to remember that displacement is a vector. As well as measuring the magnitude of the displacement, we must also specify that the displacement is in this direction. If we were to measure the change in displacement with time for this person, we would find their speed in this one particular direction. This is consistent with the definition of velocity we’ve been given.

So option (B) is the correct answer. Velocity is the change of displacement with time.

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