Video Transcript
The toy car shown was traveling at
a uniform speed before we started to measure its speed by recording its position
each second. What was the average speed of the
car during the time that the speed was measured?
Looking at the diagram, we know
that up until this moment when the measuring began, the car was moving along at a
uniform, or constant, speed. That means it was traveling equal
intervals of distance over equal intervals of time. But let’s look to see what happens
after we start measuring the car’s motion. After one second of time, the car
has moved one meter of distance. But then look at this. After two seconds of time, the
car’s position is here, which is greater than one meter of distance from its
position after one second. And then over the last second of
time measured, the car moves some distance so that its total distance from when the
measuring started is one meter plus one meter plus one meter, or three meters.
Over the three seconds of time for
which the car’s motion was measured, we want to know its average speed. We can begin solving for this by
recalling that the average speed of an object 𝑣 is equal to its change in distance
divided by its change in time. It’s worth pointing out that these
changes we’re talking about are total changes. That is, in the case of our car,
Δ𝑑 is the total change in distance the car experiences. That’s three meters as we’ve
seen. And then Δ𝑡 is the total
corresponding change in time, and we see that there are three seconds of total time
elapsed.
Δ𝑑 is three meters and Δ𝑡 is
three seconds. When we calculate this fraction, we
solve for the average speed of the car over the measured time interval. Three divided by three is one so
that average speed is one meter per second. Note that because this is an
average speed, we never actually had to figure out how far this distance here is,
that is, how much farther than one meter the car traveled between one second of time
and two seconds. To find average speed, we only
needed to know total change in distance and total change in time. As we’ve seen, that average speed
is one meter per second.
