# Question Video: Calculating Acceleration Given Initial and Final Speed Science

A train is moving at a speed of 5 meters per second. After accelerating uniformly for 3 seconds, the train has a speed of 20 meters per second. What is the acceleration of the train?

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### 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.