Question Video: Finding the Average Velocity of a Falling Body

If a body, which was dropped from a building, took 3 seconds to reach the ground, find its average velocity as it fell. Let the acceleration due to gravity ๐‘” = 9.8 m/sยฒ.

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Video Transcript

If a body, which was dropped from a building, took three seconds to reach the ground, find its average velocity as it fell. Let the acceleration due to gravity ๐‘” equal 9.8 meters per second squared.

Okay, so in this question, what we have is a body being dropped from a building. So, in the little sketch here, weโ€™ve got here our body being dropped from a building. What we can see is because itโ€™s traveling downwards, as itโ€™s come from the edge of a building, then this means that the positive direction weโ€™re gonna consider is the direction towards the ground.

We also know that its acceleration due to gravity is 9.8 meters per second squared. And this is a constant acceleration. So therefore, we know thatโ€™s a constant-acceleration problem. So, we can use our ๐‘ ๐‘ข๐‘ฃ๐‘Ž๐‘ก equations. And the equations of constant acceleration are often known as the ๐‘ ๐‘ข๐‘ฃ๐‘Ž๐‘ก equations because of our variables. We have ๐‘  which is our displacement, ๐‘ข our initial velocity, ๐‘ฃ our final velocity, ๐‘Ž our acceleration, and ๐‘ก our time.

Well, in this problem, we donโ€™t know ๐‘  because thatโ€™s our displacement cause we donโ€™t know how far it is from the top of the building to the ground. Well, we know that ๐‘ข, our initial velocity, is zero. And thatโ€™s cause the body is dropped from a building. So therefore, it was stationary at the beginning. We donโ€™t know ๐‘ฃ, our final velocity. We know that the acceleration is 9.8 because itโ€™s the acceleration due to gravity. And itโ€™s gonna be positive 9.8 because weโ€™ve decided that the downward direction is our positive direction. And the ๐‘ก, our time, is equal to three. And thatโ€™s because it took three seconds to reach the ground.

Okay, great. So now, whatโ€™s the next step? Well, what we have are five different constant-acceleration equations. We actually have different versions of these as well. Sometimes, people rearrange them. But these are often the five that we use. So, weโ€™ve got ๐‘ฃ equals ๐‘ข plus ๐‘Ž๐‘ก. ๐‘ฃ squared equals ๐‘ข squared plus two ๐‘Ž๐‘ . ๐‘  equals ๐‘ข๐‘ก plus half ๐‘Ž๐‘ก squared. ๐‘  equals ๐‘ฃ๐‘ก minus a half ๐‘Ž๐‘ก squared. And ๐‘  equals a half multiplied by ๐‘ข plus ๐‘ฃ multiplied by ๐‘ก.

Well, first of all, what weโ€™re gonna try to do is find ๐‘ , our displacement. And we know ๐‘ข, ๐‘Ž, and ๐‘ก. So therefore, what weโ€™re gonna do is weโ€™re gonna use equation three, ๐‘  equals ๐‘ข๐‘ก plus a half ๐‘Ž๐‘ก squared. So, what we get when we substitute in our values is ๐‘ , which is what weโ€™re looking for, is equal to zero multiplied by three โ€” cause thatโ€™s our ๐‘ข multiplied by our ๐‘ก โ€” plus and then weโ€™ve got a half multiplied by 9.8 multiplied by three squared. So what weโ€™re gonna get for ๐‘ , our displacement, is zero plus 4.9 multiplied by nine, which is gonna be equal to 44.1 meters. So great, weโ€™ve now found our displacement.

Well, have we finished there? Have we solved the problem? Oh, no because what weโ€™re looking for is the average velocity. But what we have is a formula to help us. And what that tells us is that the average velocity is equal to the total displacement over time, which is going to be equal to 44.1 over three. So, this is gonna give us a final answer of 14.7 meters per second. And this is going to be the average velocity of the body as it fell.

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