Video Transcript
A car follows the red line
shown. Which has the greater magnitude,
the car’s speed or its velocity? (A) Speed, (B) velocity.
This question is asking us about
the motion of a car that’s shown in the diagram. Notice what the car does to get
from the initial position to the final position. The car initially travels to the
right, away from its initial position. Then at this point, it turns around
before traveling back in the opposite direction, to the left, to reach its final
position. Let’s label the length of this path
followed by the car as 𝑑. This is equal to the distance
traveled by the car. The displacement of the car after
it has traveled this distance is the vector directed from the initial position to
the final position. We’ve labeled the magnitude of this
displacement as 𝑥. We can see that the displacement 𝑥
is smaller in magnitude than 𝑑, the distance.
Now let’s recall that the speed of
an object is equal to the distance traveled divided by the time taken, while
velocity is equal to the displacement divided by the time taken. Clearly, the time taken is the same
in both cases. It’s the time that the car takes to
get from the initial position to the final position. So, since the magnitude of the
displacement 𝑥 is smaller than the distance traveled 𝑑, then the magnitude of the
velocity must be smaller than the speed of the car. We have therefore found that the
car’s speed has a greater magnitude than the car’s velocity. That means we can identify the
correct answer as option (A) speed.
