Video Transcript
Which of the following is a correct
formula for velocity? (A) Velocity equals displacement
divided by time. (B) Velocity equals distance
divided by time.
So, we’re being asked here to
identify the correct formula for velocity. We’ve been given one formula
involving the quantity displacement and another involving the quantity distance. Let’s recall that displacement is
the difference in position from a starting point to an endpoint without considering
the path that has been taken. Distance traveled, on the other
hand, is the length of the path traveled to get from one point to another.
Suppose we have an object that
starts at this point and ends up at this point by traveling along this path. The distance traveled is the length
of the path. The displacement is the arrow
pointing from the start position to the end position. The arrow has a length, which is
the magnitude of the displacement, and a direction, which is the direction of the
displacement. Since displacement contains both
the magnitude and direction of position change, this makes it a vector quantity. Meanwhile, a distance is just the
length of the path taken, which is simply a magnitude, making it a scalar
quantity.
Now let’s recall that velocity is a
vector quantity. So it has to have a direction as
well as a magnitude. Looking at the two options we’ve
been given for a formula for velocity, in the case of (B), we are dividing the
distance traveled, which is a scalar quantity, by another scalar quantity, time. The result of dividing a scalar
quantity by another scalar quantity must be a scalar quantity with no directional
information. Equation (B) is, in fact, the
formula for the scalar quantity speed.
Equation (A), on the other hand,
divides the vector quantity displacement by the scalar quantity time. Dividing a vector by a scalar gives
a result that is a vector quantity with both a magnitude and direction. The particular vector quantity that
we get when we divide displacement by time is velocity. We know then that the correct
answer is option (A). The correct formula for velocity is
velocity equals displacement divided by time.
