Putting it all together (calc and physics)

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In summary: You can then rearrange it to get the familiar equations for position, velocity, and acceleration.In summary, the conversation is about relating calculus concepts to physics, particularly in regards to the equation Vfx^2=Vix^2+2a(delta x). The equation is a second derivative of a position function and is used to find acceleration in kinematic motion with constant acceleration. The equation can be derived by integrating and rearranging the second derivative of position with respect to time.
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LT72884
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Ello all. Ok so I am excited. i am taking my first ever physics class, calc based. SO I am trying to relate things from calc to physics because i am some what confused.

In calc we learned that if you have P(t)= t^2 + 5t +6

this is a position function. You plug in time (t) and it will give heght P(t) back. I also know if oyu take the deriv of said function and then plug in time (t), you get velocity. Take second deriv and plug in time (t) if applicable and you get acceleration in m/s^2

thats all fine and cool. but now I am given some wacked out equations

for example. i was sked to find acceleration of an ice skater after she hits a rough patch of ice. I got the answer right because it is just plug and chug, however, i don't like plug and chug. i want to know what's going on

the equation i used was

Vfx^2=Vix^2+2a(delta x)

my question is this. is the above equation a second deriv of some funky P(t) function? How is the above equation related to derivs? How did they come up with said equation. my book does not say, it just gives the equation.

im trying to relate the equation to calculs so i can understnad this better.

i do know that with position vs time graphs, where are looking at measurements of velocity, and with velocity vs time graphs, we are looking at measurments of acceleration.

thanks
 
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1. How are calculus and physics related?

Calculus and physics are closely related because calculus provides the mathematical tools for understanding and analyzing the physical world. Many physical laws and phenomena can be described and predicted using calculus, making it an essential tool in physics.

2. What are some common applications of calculus in physics?

Some common applications of calculus in physics include calculating the velocity and acceleration of an object, determining the rate of change of physical quantities, and finding the area under a curve to represent physical quantities such as work and energy.

3. How can calculus be used to solve physics problems?

Calculus can be used to solve physics problems by setting up mathematical equations that represent the physical situation, taking derivatives and integrals to find rates of change or areas under curves, and solving for the unknown variables using algebraic manipulation.

4. Can calculus be used to understand more complex physical phenomena?

Yes, calculus is a powerful mathematical tool that can be used to understand and analyze complex physical phenomena. Many advanced topics in physics, such as electromagnetism and quantum mechanics, rely heavily on calculus for their mathematical foundations.

5. Is a strong understanding of calculus necessary for studying physics?

While a strong understanding of calculus is not required for introductory physics courses, it is essential for higher-level physics courses and research. Many of the fundamental principles and equations in physics are based on calculus, so a strong foundation in calculus is important for a deeper understanding of physics.

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