### Video Transcript

A train is moving at a speed of
five meters per second. After accelerating uniformly for
three seconds, the train has a speed of 20 meters per second. What is the acceleration of the
train?

In this question, we’ve been asked
to find the acceleration of a train. We’re given its initial speed,
final speed, and the time it takes to reach its final speed. Let’s recall the equation for
acceleration. Acceleration is equal to the change
in speed divided by the time taken for the change in speed to occur, which can be
written mathematically like this. These triangles are Greek symbols
called 𝛥’s, which are often used to indicate a change in some quantity.

In order to calculate the
acceleration, we need to know the change in speed, 𝛥𝑣, and the change in time,
𝛥𝑡. Now, the train’s change in speed is
equal to its final speed minus its initial speed. We can write this mathematically as
𝛥𝑣 equals 𝑣 sub f minus 𝑣 sub i, where 𝑣 sub f is the final speed and 𝑣 sub i
is the initial speed. We know that the final speed of the
train is equal to 20 meters per second and the initial speed of the train equals
five meters per second. So the change in speed, 𝛥𝑣, is
equal to 20 meters per second minus five meters per second, which gives us a change
in speed of 15 meters per second.

The question tells us that it took
three seconds for this change in speed to occur. So, the change in time, 𝛥𝑡, is
equal to three seconds. If we substitute these values for
𝛥𝑣 and 𝛥𝑡 into the equation for acceleration, we get that the acceleration of
the train, represented by 𝑎, is equal to 15 meters per second divided by three
seconds.

Before we work this out, let’s take
a moment to think about the units here. On the right-hand side of the
equation, we have units of meters per second divided by units of seconds. This is equal to meters per second
squared, which is a good sign because meters per second squared are the correct
units of acceleration.

Now let’s finish solving this
equation. We have that the acceleration of
the train is equal to 15 meters per second divided by three seconds. This equals five meters per second
squared, so we have our answer. The acceleration of the train is
five meters per second squared.