Video Transcript
Velocity is equal to the distance
covered over a period of time. Which of the following is not a
unit of velocity? Is it (a) centimeters per second,
(b) meters per second, (c) meters per second squared, (d) meters per minute, or (e)
kilometers per hour?
Since velocity is equal to the
distance covered over a period of time, velocity š£ is given by the equation š£
equals š over š”, where š is the distance and š” is the time elapsed. We can determine the dimension of
velocity by performing dimensional analysis on this equation. All this means is replacing every
variable on the right-hand side of the equation with its dimension. So, in this case, the distance š
has dimension length šæ and the time elapsed š” of course has dimension time š. Both sides of the equation must
have the same dimension. Therefore, the dimension of š£ must
be the same as the dimension of š over š”, šæ over š.
We can now compare this with every
one of our answers to see which one does not have units representing dimension L
over š. So, for answer (a), we have the
centimeter, which is a multiple of the meter, the base unit for length. And we have second, which is the
base unit for time. So answer (a) is šæ over š. So this is indeed a unit for
velocity.
For answer (b), we just have the
base unit for length over the unit for time. So this is also a unit for
velocity. For answer (c), we have the base
unit for length, the meter, divided by the base unit for second squared. So the dimension is šæ over š
squared. Therefore, (c) is not a unit for
velocity. For completeness, for answer (d),
we have the base unit for length, again, divided by the minute, which is a multiple
of the second. So we have length over time once
again. And likewise, for (e), we have the
kilometer, a multiple of the meter, divided by the hour, a multiple of the
second. So we once again have šæ over š. Therefore, our answer is (c). Meters per second squared is not a
unit of velocity.
