Video Transcript
The arrows shown represent velocities. The black arrow represents a velocity of 10 meters per second. Which of the following velocities could the red arrow represent? (A) Five meters per second, (B) negative five meters per second.
Okay, so we’ve got a diagram showing two arrows, one of which is black and the other is red. We’re told that these two arrows represent velocities. And we can recall that velocity is a vector quantity, which means that it has both a magnitude and a direction. When a vector quantity is represented by an arrow like the ones in this diagram, the length of the arrow tells us about the magnitude of the vector. And the direction of the arrow gives the direction of the vector. If we look at the arrows in this diagram, we can see that the red arrow is shorter than the black arrow. Since the black arrow is longer and the red arrow is shorter, this means that the red arrow must represent a velocity with a smaller magnitude than the black arrow.
Since we’re told in the question that the black arrow represents a velocity of 10 meters per second, then we can see that both the available options, five meters per second and negative five meters per second, are velocities with a smaller magnitude than this. So, on the basis of magnitude, either of these two answers could be the velocity represented by the red arrow.
The other thing to consider though is the direction of the arrows in the diagram. We can see that the black arrow is pointing to the right, and we’re told that this arrow represents a velocity of 10 meters per second, which is a positive value. This means that on the horizontal left–right axis, right must be the positive direction. This tells us that all velocities represented by arrows pointing to the right will have positive values. And similarly, all velocities represented by arrows pointing in the opposite direction to the left must be negative.
We can see from the diagram that the red arrow is pointing to the left, and so it must represent a velocity with a negative value. The velocity given in option (A) is five meters per second, which is a positive value of velocity, so this cannot be our answer. Meanwhile, the value given in option (B) is negative five meters per second, which is a negative velocity. And so this must be our answer to the question. The velocity that could be represented by the red arrow is negative five meters per second. This is the answer given here in option (B).
