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!

Saturday, October 29, 2011

Yea Week 3!

Last week we learned about the calculus of motion and the derivatives of trig functions. I think you all did pretty well with the derivatives of trig functions! Remember that unit circle! This week we are going to learn about the chain rule and implicit differentiation. Exciting! Don't forget that there is a short quiz over section 3.4 on Monday. To test your knowledge (without looking at your notes) describe to me how velocity and acceleration are related to the position of an object, in terms of derivatives. Also tell me how you would determine the speed of an object at a particular instant if you were given the position function, s(t).
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12 comments:

  1. aiden wangOctober 30, 2011 at 12:21 PM

    velocity describe the change of position while acceleration describe the change of velocity. the time-velocity function is the derivative of time-position function. the time-acceleration function is the derivative of time-velocity function. so the velocith function is the first derivative of the position function.and the acceleration one is the second. that's all.

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  2. AnonymousOctober 31, 2011 at 8:01 AM

    Speed function is the basic function, velocity function is the derivative of Speed function, acceleration is the second derivative of speed function as well as it is the first derivative of velocity function ! That's all !

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  3. Mrs. YoungOctober 31, 2011 at 8:05 AM

    Nicholas, I believe you have the speed function confused with the position function. The position function is the basic function. Remember that speed is just the absolute value of velocity!

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  4. Krista WoodOctober 31, 2011 at 9:59 AM

    The velocity function is the first derivative of the position function and the acceleration function is the first derivative of the velocity function so therefore it is the second derivative of the position function. If I was given the position function you could find the speed by first finding the velocity and then taking the absolute value of your answer.

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  5. Mrs. YoungNovember 1, 2011 at 9:19 AM

    Perfect Krista! Thanks for answering all of my questions.

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  6. Anna SchrammNovember 1, 2011 at 1:40 PM

    Velocity is the first derivative of the position function and acceleration is the second derivative of the position function since acceleration is the first derivative of the velocity function. Also, to find the speed of an object, you would first find the derivative of the position function to give you velocity. Then, all you have to do to find the speed from the velocity is take the absolute value of it.

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  7. AnonymousNovember 2, 2011 at 9:51 AM

    Velocity is the first derivative of the position function and acceleration is the first derivative of the velocity which is the second derivative of the position. To find the speeed at a particular instant, you would have to find the velocity and take the absolute value of the velocity.

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  8. Alexa SpudieNovember 2, 2011 at 4:40 PM

    Velocity is the first derivative of the position function. Acceleration is the first derivative of the velocity function, or the second derivative of the position function. To find the speed at a particular instant, you would find the derivative of the position function, plug in the time in for t, and solve. Then you would take the absolute value of that answer to get the speed.

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  9. Ukbin KwonNovember 3, 2011 at 7:21 PM

    Velocity is first derivative of position function and acceleration is second derivative of position function. In order to find the particular velocity with given function, plug in the time in for t and put it in first derivitive of position functon. It will give me the particular velocity, and speed will be the absolute value of the velocity.

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  10. Caroline KangNovember 3, 2011 at 7:33 PM

    Velocity is the first derivatie of the position function and acceleration is second derivative of the position function also first derivative of the velocity. To find the speedat a particular instant, find the velocity and put absolute value sign both side.

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  11. Nate LyellNovember 4, 2011 at 9:54 AM

    The velocity function is the first derivative of the position function and the acceleration is the second derivitive of the position function (or the first derivitive of the velocity function) to find the speed of an object at a particular time given its position function, I would take the derivitive of the positionfunction to obtain the velocity function and then plug in the value of t and then take the absolute value of my answer.

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  12. Alicia WhaJung HanNovember 4, 2011 at 5:17 PM

    Velocity function is first derivative of position function, and acceleration function is second derivative of position function. To find the speed of the function, you need to find the velocity first and put absolute value on it because velocity also shows direction of the object but not speed.

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