A moving hockey puck encounters a patch of rough ice and slides 90cm before coming to a full stop. Assuming a constant deceleration of 8 m/s 2 , what was the puck's initial speed?

Alright, guys. Let's get some more practice. Let's keep going. We've got a hockey puck that's encountering a patch of rough road. It slides to a full stop. And what is the puck's initial speed? So let's just draw a quick little sketch of what's going on here. We've got a hockey puck that looks like this. And it's gonna slide across some road, and it's gonna come to a stop right here. So it's got some initial velocity in this direction, but then it's gonna come to a stop. And what that means is that the final velocity is equal to 0. And we have the constant deceleration of 8 meters per second squared. What that means is that the actual acceleration points to the left. The velocity initial is to the right, so it's decelerating or slowing down, so the acceleration has to point backwards. Because of that, it's not gonna be 8 meters per second squared. Now we actually have to talk about the sign. It's gonna be negative 8 meters per second squared. So sometimes you're gonna have to infer the direction from the text. And so basically, now we've just gotta solve for the puck's initial speed. We also know that this distance over here is 90 centimeters, which equals 0.9 meters. Okay. So now we just gotta list our variables, delta x, v naught, v, acceleration, and time. So we've got delta x. We know this is 0.9. Our initial velocity is actually what we're gonna be looking for. Right? What's the puck's initial speed? We We know the final velocity is gonna be 0. We know the acceleration is equal to negative 8. So now that we got our variables, we've also identified the known and the target variables, Now we just gotta pick the one without the ignored variable. In this case, since we have our 3 out of 5 variables, and we're looking for the initial velocity, ignored variable is going to be the time. So that means that we go and look through the equation that doesn't have time. And if you guys remember, that's gonna be equation number 2. That's the timeless formula, as they call it. So this is gonna be equation number 2. We've got v squared equals v initial squared plus 2 a times delta x. We know that the final velocity is gonna be 0 squared. The initial velocity is actually what I'm looking for here. And so now, we've got 2 times the negative eight times 0.9. And so, if you work this out, what you're gonna get is 0 squared is equal to v naught squared plus Or actually, that's gonna be minus because of the minus sign. 14.4. And so, cool. Now we've, basically, we just move this to the other side, and we get that 14.4 is equal to V naught squared. And And now we just take the square root. So that means that v naught is equal to, and we're gonna get the square roots of 14.4, which is going to be 3.79 negative, or it could be 3.79 positive. So now we just have to figure out which one of these makes sense. Remember that when you take the square root of any number, you're gonna get a positive and negative. So for example, over here, the square root of 9 is not just 3, it's also negative 3 because you can also multiply that by itself and you'll also get 9. So which one of these makes sense? Well, a negative speed would mean that it's going in the backwards direction and that doesn't make any sense. So that means that this is going to the left, which doesn't make any sense because we know our hockey puck should be moving to the right. So that means that our real answer is actually going to be this guy over here. It's gonna be plus 3.79 and that's gonna be meters per second for the units. Alright guys, that's it for this one. Let's keep going.

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A moving hockey puck encounters a patch of rough ice and slides 90cm before coming to a full stop. Assuming a constant deceleration of 8 m/s2, what was the puck's initial speed?

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A moving hockey puck encounters a patch of rough ice and slides 90cm before coming to a full stop. Assuming a constant deceleration of 8 m/s², what was the puck's initial speed?