Video Transcript
Which of the following is a correct
unit for acceleration? (A) Meters per second, (B) meters
per second squared, (C) meters per second quantity squared.
To begin figuring this out, let’s
remember what acceleration is. Mathematically, acceleration is a
change in speed, Δ𝑣, divided by a change in time. So let’s say we had an object which
at a time of zero seconds was moving at a speed of four meters per second. And then two seconds later, the
object is moving at seven meters per second. We can calculate the object’s
acceleration using this relationship. We’ll do this so we can see what
the units of acceleration can be. All right, in the numerator of this
fraction, we want to put the change in our object’s speed. That will be equal to its final
speed, seven meters per second, minus its initial speed of four meters per
second.
Next, let’s think about Δ𝑡, the
time that has elapsed. This is equal to two seconds minus
zero seconds. So this fraction, the acceleration
of our object, is equal to three meters per second divided by two seconds. And here, we’re really only paying
attention to the units. We have the units of speed, meters
per second, divided by the units of time, seconds. The question is, to which one of
our three answer options does this correspond? We can see right away that we won’t
choose option (A). A unit of meters per second is a
speed, not a change in speed over time.
To see how to choose between
options (B) and (C), let’s work on this expression a bit. Right now, we have a fraction here
and we have a fraction here. We can make it though so that we’re
only working with one overall fraction. To do that, we’re going to multiply
the top and bottom of this overall fraction by the same value. We can choose this value to be
whatever we want.
But if we make a specific choice
and choose it to be one over seconds, then when we multiply in the denominator, we
get seconds divided by seconds, which simplifies to one. Then in the numerator, we multiply
meters by one and seconds by seconds. That gives meters divided by
seconds times seconds or meters per second squared. Dividing meters per second squared
by one doesn’t change the value at all. So we’re free to remove the
one. This leaves us with meters per
second squared, option (B).
Note that this is different from
option (C). In option (C), we see meters per
second quantity squared, which means we square both numerator and denominator. That gives us meters squared per
second squared, while a correct unit for acceleration is meters per second
squared.
