- #1
Help for Dynamics Continuous Motion
- Thread starter JamieShumJr
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In summary, the conversation discusses obtaining a figure in a red circle and the use of the product rule in integration. It is discovered that the 0.8 coefficient was neglected during integration, leading to the incorrect result. The basic rule of integration is applied and the correct answer is obtained. The conversation then moves on to discuss the derivation of a -1/60 term, which is obtained by evaluating the integral at t and 0 and subtracting the results.
- #2
tiny-tim
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Welcome to PF!
Hi JamieShumJr! Welcome to PF!
You're asking why is ∫ (0.8t + A)-1/2 dt = (2/0.8)(0.8t + A)1/2 …
apply the https://www.physicsforums.com/library.php?do=view_item&itemid=353" twice …
if you differentiate the RHS, you get an extra 0.8 from the t, and an extra 1/2 from the power, = (0.8/2)
Hi JamieShumJr! Welcome to PF!
JamieShumJr said:
You're asking why is ∫ (0.8t + A)-1/2 dt = (2/0.8)(0.8t + A)1/2 …
apply the https://www.physicsforums.com/library.php?do=view_item&itemid=353" twice …
if you differentiate the RHS, you get an extra 0.8 from the t, and an extra 1/2 from the power, = (0.8/2)
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- #3
JamieShumJr
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tiny-tim said:Hi JamieShumJr! Welcome to PF!
You're asking why is ∫ (0.8t + A)-1/2 dt = (2/0.8)(0.8t + A)1/2 …
apply the https://www.physicsforums.com/library.php?do=view_item&itemid=353" twice …
if you differentiate the RHS, you get an extra 0.8 from the t, and an extra 1/2 from the power, = (0.8/2)
Thanks a lot!
I neglected the 0.8 during the integration. Got it already. Forgotten the basic rule of integration.
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- #4
mintz
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may i know from same question as above shown, how to get the -1/60 at the end there?
- #5
tiny-tim
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welcome to pf!
hi mintz! welcome to pf!
the ##|^t_0## at the end of the previous line means you have to evaluate it at t and at 0, and subtract
hi mintz! welcome to pf!
mintz said:
the ##|^t_0## at the end of the previous line means you have to evaluate it at t and at 0, and subtract
- #6
mintz
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tiny-tim said:hi mintz! welcome to pf!
the ##|^t_0## at the end of the previous line means you have to evaluate it at t and at 0, and subtract
oh~okie~thanks! i made mistake that evaluate at 0 whole things became 0~
thanks anyway!=D
FAQ: Help for Dynamics Continuous Motion
What is Dynamics Continuous Motion?
Dynamics Continuous Motion refers to the study and analysis of objects in motion, specifically in relation to forces acting upon them. It is a branch of physics that focuses on understanding and predicting the behavior of moving objects.
Why is Dynamics Continuous Motion important?
Understanding Dynamics Continuous Motion is important because it helps us explain and predict the motion of objects in our everyday lives, from the movement of cars and planes to the orbit of planets. It also allows us to design and build machines and structures that can withstand various forces and movements.
What are some real-world applications of Dynamics Continuous Motion?
Some real-world applications of Dynamics Continuous Motion include building bridges, designing roller coasters, creating efficient transportation systems, and understanding the behavior of projectiles in sports like baseball and basketball.
What are the main principles of Dynamics Continuous Motion?
The main principles of Dynamics Continuous Motion include Newton's Laws of Motion, which describe the relationship between an object's motion and the forces acting upon it, as well as concepts such as friction, inertia, and momentum.
How can I apply Dynamics Continuous Motion in my own experiments or projects?
To apply Dynamics Continuous Motion in your own experiments or projects, you can start by identifying the forces acting upon an object and analyzing how they affect its motion. You can also use mathematical equations and models to predict the behavior of the object. Additionally, you can use various tools and technologies, such as motion sensors and computer simulations, to gather data and visualize the motion of objects.
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