At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
The velocity of a particle = i + 2t j
The acceleration of a particle = 2 j
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
Here,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
We have to find, the velocity, acceleration, and speed of a particle with the given position function.
What is Velocity of a particle with the given position function?
The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.
Now,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]
The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]
Hence, The velocity of a particle = [tex]i + 2t j[/tex]
The acceleration of a particle = [tex]2 j[/tex]
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
Learn more about the velocity visit:
https://brainly.com/question/18566194
#SPJ4
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
