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 𝑔 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, we’ve got here our body being dropped from a building. What we can see is because it’s traveling downwards, as it’s come from the edge of a building, then this means that the positive direction we’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 that’s a constant-acceleration problem. So, we can use our 𝑠𝑢𝑣𝑎𝑡 equations. And the equations of constant acceleration are often known as the 𝑠𝑢𝑣𝑎𝑡 equations because of our variables. We have 𝑠 which is our displacement, 𝑢 our initial velocity, 𝑣 our final velocity, 𝑎 our acceleration, and 𝑡 our time.
Well, in this problem, we don’t know 𝑠 because that’s our displacement cause we don’t know how far it is from the top of the building to the ground. Well, we know that 𝑢, our initial velocity, is zero. And that’s cause the body is dropped from a building. So therefore, it was stationary at the beginning. We don’t know 𝑣, our final velocity. We know that the acceleration is 9.8 because it’s the acceleration due to gravity. And it’s gonna be positive 9.8 because we’ve decided that the downward direction is our positive direction. And the 𝑡, our time, is equal to three. And that’s because it took three seconds to reach the ground.
Okay, great. So now, what’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, we’ve got 𝑣 equals 𝑢 plus 𝑎𝑡. 𝑣 squared equals 𝑢 squared plus two 𝑎𝑠. 𝑠 equals 𝑢𝑡 plus half 𝑎𝑡 squared. 𝑠 equals 𝑣𝑡 minus a half 𝑎𝑡 squared. And 𝑠 equals a half multiplied by 𝑢 plus 𝑣 multiplied by 𝑡.
Well, first of all, what we’re gonna try to do is find 𝑠, our displacement. And we know 𝑢, 𝑎, and 𝑡. So therefore, what we’re gonna do is we’re gonna use equation three, 𝑠 equals 𝑢𝑡 plus a half 𝑎𝑡 squared. So, what we get when we substitute in our values is 𝑠, which is what we’re looking for, is equal to zero multiplied by three — cause that’s our 𝑢 multiplied by our 𝑡 — plus and then we’ve got a half multiplied by 9.8 multiplied by three squared. So what we’re gonna get for 𝑠, our displacement, is zero plus 4.9 multiplied by nine, which is gonna be equal to 44.1 meters. So great, we’ve now found our displacement.
Well, have we finished there? Have we solved the problem? Oh, no because what we’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.