A train travels 160 meters at a
uniform speed of eight meters per second. The position of the train at two
different times is shown. How much time does the train take
to travel the distance between the positions?
In this question, we are asked to
find the time it takes this train to travel the distance of 160 meters, given that
the train is traveling at a uniform speed of eight meters per second.
First, we should recall the
equation for speed. Speed is equal to the distance
traveled divided by the time it takes to travel that distance. For this question, the values of
speed and distance are known, but the value of time is unknown.
Let’s make time the subject of the
equation that relates speed, distance, and time. Making time the subject of the
equation involves several steps. The first step is multiplying both
sides of the equation by time. This first step shows that the
speed multiplied by the time traveled for equals the distance traveled. However, we wish to find the time
traveled for. To do this, we must now divide both
sides of the equation by the speed. When we do this, we get the
equation time is equal to the distance traveled, 160 meters divided by the speed
that the train is moving, eight meters per second.
Notice that the units on the
right-hand side of the equation are meters divided by meters divided by seconds. Remember that when we have a
fraction with another fraction in the denominator, the denominator of the bottom
fraction moves to the numerator of the entire fraction. And we are left with meters seconds
divided by meters. The units of meters cancel. And so we are left with seconds on
the right-hand side of the equation. The left-hand side of the equation
is a time, which can be written as a number of seconds. So seconds matches the units for
the right-hand side of the equation.
We see then that the value of time
equals 160 divided by eight, and the unit for this value is seconds. This equals 20 seconds. So the time taken for the train to
travel between the two positions shown is 20 seconds.