Velocity of an Object given its position as a function of time

In summary, Attached is the problem and my work through the problem. I got the problem correct, but my teacher said this could be done quicker on a calculator. Any idea how it could be done quicker.Check your relevant equations.
  • #1
Strand9202
10
2
Homework Statement
Velocity of an object: Picture of problem and work attached
Relevant Equations
Speed =s(t)
Acceleration = s'(t)
Velocity = s"(t) or a'(t)
Attached is the problem and my work through the problem. I got the problem correct, but my teacher said this could be done quicker on a calculator. Any idea how it could be done quicker.

Screen Shot 2021-02-08 at 8.23.12 PM.png

Screen Shot 2021-02-08 at 8.23.25 PM.png
 

Attachments

  • 63452099186__DCDFFA52-49D9-4E49-B69A-84ED1CA44B81.jpeg
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  • 63452097838__A519283C-EC71-4527-BAEA-EDB73A167AA7.jpeg
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Last edited:
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  • #2
Check your relevant equations.
In #6, s(t) is the position, not the speed (an unfortunate choice of variables).
Speed is the derivative of position
Acceleration is the derivative of speed.
 
  • #3
FactChecker said:
Check your relevant equations.
In #6, s(t) is the position, not the speed (an unfortunate choice of variables).
Speed is the derivative of position
Acceleration is the derivative of speed.
My work for number 6 is correct. My teacher checked it, but they said I could have used a calculator to find it quicker.
 
  • #4
Sorry, I missed that your work was correct. In any case, I stopped reading when I saw that your "Relevant Equations" are all wrong.
Do you have a graphing calculator? Maybe your teacher means that you can look at the graph of position and determine the answer.
 
  • #5
Strand9202 said:
I got the problem correct, but my teacher said this could be done quicker on a calculator.
Well, lots of things can be done more quickly on a calculator, but so what? If I were the teacher, and I've taught many calculus classes, I would be happy with your work.
As a PF member, I'm not quite as happy, since your images are all rotated by 90°. Your handwriting is very clear, though, and the images are well-lit.
 
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  • #6
Mark44 said:
Well, lots of things can be done more quickly on a calculator, but so what? If I were the teacher, and I've taught many calculus classes, I would be happy with your work.
As a PF member, I'm not quite as happy, since your images are all rotated by 90°. Your handwriting is very clear, though, and the images are well-lit.
Sorry I thought I put the right side pictures up. I reedited and attached the correct ones.
 
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1. What is the equation for calculating velocity using position as a function of time?

The equation for calculating velocity using position as a function of time is v = (xf - xi) / (tf - ti), where v is velocity, xf and xi are final and initial positions, and tf and ti are final and initial times.

2. How does the velocity of an object change over time?

The velocity of an object can change over time if its position changes at a varying rate. For example, if an object is accelerating, its velocity will increase over time.

3. Can an object have a constant velocity if its position is changing?

Yes, an object can have a constant velocity even if its position is changing. This is possible if the object is moving at a constant speed in a straight line.

4. How is velocity related to acceleration?

Velocity and acceleration are directly related. Acceleration is the rate of change of velocity over time. This means that if an object's velocity is changing, it is accelerating.

5. Can the velocity of an object be negative?

Yes, the velocity of an object can be negative. This means that the object is moving in the opposite direction of its positive direction. For example, if an object is moving to the left, its velocity will be negative.

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