106. Motion Along a Line The graphs in Exercises 105 and 106 s...

Question

106. Motion Along a Line The graphs in Exercises 105 and 106 show the position s=f(t) of an object moving up and down on a coordinate line. At approximately what times is the (b) velocity equal to zero?
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Accepted Answer

Below there, today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A particle moves along a line, and its displacements in units of meters is a function of time T in units of seconds, which can be written as S equals F T, is described by the graph shown. At what times is the particle monetarily at rest? Awesome. So it appears for this particular problem, we're ultimately trying to determine at what times this particle is momentarily at rest, meaning when it's at rest, it means that the particle is not moving. So now that we know that we're ultimately trying to figure out at what time intervals this particular particle is at rest momentarily, meaning that it's not permanent. It's just for like a brief moment in time, it's at rest, meaning it's not moving. So we're trying to figure out what particular times this particle during its path when it moves along a line that it's not moving, it's at rest. So, with that said, our first step now is we need to look at our graph that is provided to us. As you can see, our Y axis is denoted by S. The displacement, which is in units of meters, and our X-axis denotes the time T in units of seconds. Fantastic. And then we have our particle's path along the line, represented by a red curve. Now as you can see, it starts from rest at the origin point 0.0, and then it starts to move. And increase, increase, increase, and then it starts to dip down where it's momentarily appears to be at rest because it's goes, and so it's not moving, so it starts from rest, and then it goes to rest again briefly, and then it goes down, down, down, down, and then it starts to curve up where it's at rest once again, and then it just keeps going, going, going up. So it so it starts from rest, then it goes up and then it might slow down, goes to rest for a little bit, then dips down and then goes up at rest again, and then it goes straight back up again. Following our red curve, and once again the curve represents S equals F T. Fantastic, and the curve is in red. So now that we have a visualization of what's happening in this particular problem, let us recall a note. Once again, the particle is momentarily at rest when its velocity is 0. So the first derivative of S with respect to T represents the velocity of the particle. That is, that V is equal to DS by DT. Fantastic. So that means that graphically, the slope of the line tangent to any time T. On a displacement versus time graph represents the velocity at that particular value of T. So, therefore, as a result, as a result, for a zero velocity, the tangent line is horizontal, meaning that the slope is zero. So the given graph has horizontal tangent lines at approximately. And it's important to note, so it's gonna be at approximately 03, and 7 seconds, and that is our final answer. we did it. So let's look at our graph. So as you can see, once again, the graph has horizontal tangent lines at approximately 0. 3 and 7 seconds. Awesome. So once again, so for a zero velocity, the tangent line is horizontal, meaning that the slope is zero. So when we do that, we will find that it's approximately at 03, and 7 seconds. And that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

106. Motion Along a Line The graphs in Exercises 105 and 106 show the position s=f(t) of an object moving up and down on a coordinate line. At approximately what times is the (b) velocity equal to zero?
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Key Concepts

Position Function

Velocity

Critical Points

Watch next

106. Motion Along a Line The graphs in Exercises 105 and 106 show the position s=f(t) of an object moving up and down on a coordinate line. At approximately what times is the (b) velocity equal to zero?<IMAGE>

Key Concepts

Position Function

Velocity

Critical Points

Watch next

106. Motion Along a Line The graphs in Exercises 105 and 106 show the position s=f(t) of an object moving up and down on a coordinate line. At approximately what times is the (b) velocity equal to zero?
<IMAGE>