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Question Video: Finding the Final Velocity of a Body Moving with Uniform Acceleration given Its Initial Velocity and the Covered Distance Mathematics

A particle was moving in a straight line with a constant acceleration of 2 cm/sΒ². Given that its initial velocity was 60 cm/s, find the velocity of the body when it was 15 m from the starting point.

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Video Transcript

A particle was moving in a straight line with a constant acceleration of two centimeters per square second. Given that its initial velocity was 60 centimeters per second, find the velocity of the body when it was 15 meters from the starting point.

We have a constant acceleration, so we’re going to use our kinematic equations. For a starting velocity 𝑣 naught, an acceleration π‘Ž, and a velocity 𝑣 after 𝑑 time units, the first equation is 𝑣 equals 𝑣 naught plus π‘Žπ‘‘. We introduce Ξ”π‘₯ to represent the displacement of the objects. And we get Ξ”π‘₯ equals 𝑣 naught 𝑑 plus a half π‘Žπ‘‘ squared. Our third equation Ξ”π‘₯ is equal to a half 𝑣 naught plus 𝑣 times 𝑑. And then we have one further equation. That is 𝑣 squared equals 𝑣 naught squared plus two times π‘Ž times Ξ”π‘₯.

Let’s list what we know about the motion of our particle. We have acceleration as two centimeters per square second, an initial velocity of 60 centimeters per second, and a displacement Ξ”π‘₯ of 15 meters. Now, in fact, our acceleration and velocity are given in centimeters per second and centimeters per square second. So, we want the units to be the same for Ξ”π‘₯. We multiply 15 by 100 and we see that that’s 1500 centimeters. We’re looking to find the velocity of the body when it’s this distance away from the starting point. Notice that that means we’re not interested in the time that this takes.

So, we go through to our four kinematic equations and we get rid of those that contain 𝑑. Well, that’s equation one, two, and three. That leaves us with just one equation, 𝑣 squared equals 𝑣 naught squared plus two times π‘Ž times Ξ”π‘₯. We’re going to substitute everything we know about the motion of our particle into this equation. When we do, we get 𝑣 squared equals 60 squared plus two times two times 1500. 60 squared is 3600. And two times two times 1500 is 6000. So, 𝑣 squared is equal to 9600.

It follows that we can solve for 𝑣 by finding the square root of both sides of our equation. 𝑣 is therefore equal to the square root of 9600. That’s 97.97 and so on. Correct to the nearest whole number, that’s 98. And we can therefore say that the velocity of the body when it’s 15 meters from the starting point is 98 centimeters per second.

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