Welcome to Mrs. Young's calculus class blog! Each week, I will start a new post. Students, you can write questions for me or chat with each other about how to solve a particular problem. As part of your class participation grade each week, every student must comment at least once to my post or another student's comment. I look forward to spending this year with you. Enjoy!

Sunday, October 7, 2012

October 8th - 12th

This week we are going to continue talking about position, velocity, and acceleration, one of the very important topics in calculus. I will also be introducing your chapter 3 project this week, which is related to these rates of change. For this week, in your own words, I'd like you to tell me the relationship between position, velocity, and acceleration. Also, if you were given a velocity versus time graph for a golf ball that has been hit into the air, where would you look to identify the times when the golf ball is moving upward? Then, I'd like you to give me another example of when the calculus of motion can be applied to the real world.
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12 comments:

  1. UnknownOctober 8, 2012 at 5:32 PM

    I think position is miter or feet, velocity is derivative of position(y') – related with speed, and acceleration is second derivative of position(y'')- rate of speed change. Also I can see the golf ball is moving upward where velocity > 0. For example, someone kick the ball. If you want to know how far the ball goes at the specific time, you can use position function. If you want to know how fast the speed at the specific time, you can use velocity. If you want to know the rate of ball’s speed change, you can use acceleration.

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  2. SarahDunn2013October 10, 2012 at 10:05 AM

    Position, velocity, and acceleration are closely related to each other. Position (s(t)) gives the location of an object at a given time. Velocity, the derivative of the position function (s'), gives the instantaneous rate of change for the object at the given time. Finally, acceleration, the first derivative of the velocity function and the second derivative of the position function (s''),gives the rate at which the velocity is changing at that time. If given a velocity versus time graph for a golf ball, all positive values of velocity would mean that the ball was traveling upwards. In other words, when the value on the y-axis is greater than zero, the ball is still traveling upward. Calculus of motion can also be used to find things such as how fast a container is being emptied if you are given the amount of water in the tank relative to the time (a position function).

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  3. BenIvanOctober 10, 2012 at 10:41 AM

    Position is simply gives you the location of the given object at a certain time. Velocity is the instantaneous rate of change for that object and can be solved by taking the derivative of the position function. Acceleration is the change in velocity at a given time, and this can be solved by taking the second derivative of the position function. The velocity/ time graph of a golf ball would show that the golf ball is traveling upward at all positive values of velocity. Another example of the calculus of motion would be someone throwing a football, and you could solve for distance at a specific time (position), maximum height, and the change of velocity over the time period that the ball is in the air (acceleration).

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  4. jacob eversoleOctober 10, 2012 at 11:39 AM

    Position is the location of an object, Velocity is the derivative of the position function, and the acceleration is the second derivative of the position function. To show that the golf ball is moving up at the positive velocity values, you would use a velocity graph. You could use the calculus of motion for the kicking of a soccer ball.

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  5. AnonymousOctober 11, 2012 at 9:19 AM

    Position is the location of an object in respect to time, velocity is the speed and direction of an object as well as the first derivative of the position function. Acceleration is an objects change in velocity over time as well as the first derivative of velocity and the second derivative of the position function.On the velocity versus time graph of the golf ball you would look to see during which time intervals is the velocity or Y-values positive and that will show when the golf ball is moving upward.Calculus of motion can be applied to the real world when solving for when does a tennis ball change direction when you throw it into the air.

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  6. UnknownOctober 11, 2012 at 3:06 PM

    position is location of an object with respect to time. velocity is the rate of change of position with reepect to time. Acceleration is the derivative of a velocity function respect to time. On the velocity versus time graph with the golf ball, to see when the golf ball is moving upward, you would look at which time intervals in which the velocity is positive. An example of calculus of motion is a volleyball player setting a ball, looking at the upward direction of the ball, and also the point where the ball starts moving downward.

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  7. Grace HillOctober 12, 2012 at 10:32 AM

    Position, velocity and acceleration are all related to each other. Position is is the location of an object with respect to time. The velocity is the derivative of the position function, and can be described as the change of position with respect to time. Acceleration is the derivative of the velocity function, and can be described as the change in velocity over time. If you were looking at a velocity time graph for the golf ball, to find when the ball is moving upward is when the graph is positive for all Y values. When the graph is negative for Y values, the ball is moving downward to indicate a negative velocity. A real world example is how quickly a car would be accelerating from rest.

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  8. Isaac BarringerOctober 12, 2012 at 10:50 AM

    The position equation will give you the position of an object at a specific time. The velocity equation, the derivative of the position equation, gives you the instantaneous rate of change over a specific time. The acceleration, the derivative of the velocity equation, shows how much the velocity is changing either over a period of time or in a specific time. For a velocity time graph, I would look at the times where the slope is positive and that will tell me that the ball is going upward. Another real world example is like if a quarterback passes the ball to his receiver, and you can create equations to represent the position, velocity, and acceleration.

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  9. Daniel BurketOctober 12, 2012 at 11:24 AM

    Position is how far away from something an object is. For example, a car might be 20 km away. Position can be either positive or negative, depending on its location (up or down, right or left). Velocity is the rate of change with direction. An example would be 40 km/h. Acceleration is the rate that the velocity changes (it is the derivative of velocity). An example would be 20 m/s².

    To find when the golf ball is moving upward in a velocity-time graph, you would look at all parts of the function above the x-axis (positive; and to the right of 0, because you cannot have negative seconds). Since velocity is speed with direction, negative velocity means travelling in the opposite direction than the positive velocity. Another real world example would be a roller coaster going over a hill. The position-time graph would show you where the roller coaster is at a specific time. The velocity-time graph would show the speed and direction at a certain time, while the derivative of that function would show the acceleration at a specific time.

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  10. UnknownOctober 12, 2012 at 11:26 AM

    position is the exact location of an object. the velocity is the derivative of the position function. the acceleration is the derivative of the velocity function or the second derivative of the position function. to figure out when the golf ball is being moved upward, you would use the positive values of the velocity graph. you can apply the calculus of motion when hitting a baseball in to the air with a bat.

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  11. Carly CannonOctober 12, 2012 at 11:36 AM

    Position is where an object is at a certain time. Position is represented as s(t) where t is time. Average velocity in relation to this is the object's change in position divided by the change in time. Average velocity is over an period of time. This is shown as s(t2)- s(t1) / t2- t1. Instantaneous velocity on the other hand is at a specific instant. In relation to position this is the derivative of the position function at that point. This would be shown as s'(t). Velocity tells both how fast the object is moving and in what direction. Acceleration is the change in velocity over time. This is the second derivative of the position function and is shown as s''(t). If you were given a velocity vs. time graph of a golf ball you would know the ball is moving upward when the velocity is positive or above the x- axis. Another real would example would be when a volleyball is set to a hitter. Here you could measure position, velocity, and acceleration.

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  12. rachel schillingOctober 19, 2012 at 11:59 AM

    Velocity is the derivative of position and acceleration is the derivative of velocity, therefore acceleration is the second derivative of position. In other words, velocity is the rate of change of the position and acceleration is the rate of change of velocity. The golf ball would be moving upward when the y values of the graph are positive. Another real world example would be a football thrown into the air. Position, velocity, and calculation can all be calculated.

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