Video Transcript
A train moves uniformly at 12
meters per second. The position of the train at two
different times is shown. What distance does the train move
between the two times?
Let’s start by taking a look at the
question and the diagram we are given. We are asked to find the distance
the train travels between the two given times. Looking at the diagram, we can see
that the difference between these two times is five seconds. The train is moving uniformly, so
it has a constant speed, which is 12 meters per second. We need to find the distance that
the train travels. Recall that speed is equal to the
distance traveled divided by the time it takes to travel that distance.
Here we have our speed, 12 meters
per second, on the left side of the equation and the unknown distance divided by the
time, five seconds, on the right side. Let’s multiply both sides of the
equation for the speed by five seconds. If we do this, the unknown distance
𝑑 will be equal to the left-hand side of the equation. We see that 12 meters per second
multiplied by five seconds is equal to the distance traveled.
When we multiply both sides of the
equation by five seconds, notice how the unit of seconds in the numerator cancels
the unit of seconds in the denominator so that we are left with just meters on the
left-hand side of the equation. The right-hand side of the equation
is a distance, which we can write as a number of meters. This means that the units on the
left-hand side of the equation match the units on the right-hand side. Now let’s multiply the left-hand
side. 12 meters per second multiplied by
five seconds is equal to 60 meters. So the distance the train moves
between the two times is 60 meters.
