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Question Video: Calculating the Travel Time of a Train That Moves Uniformly Science

A train travels 160 m at a uniform speed of 8 m/s. 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?

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Video Transcript

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.

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