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laila [671]
2 years ago
13

The position of a particle moving in the xy plane is given by the parametric equations x(t)=t^3-3t^2

Physics
1 answer:
Basile [38]2 years ago
4 0

The value of t  for which the particle is at rest is :  t = 2

<u>Given data:</u>

X = t³ - 3t²

Y = 2t³ - 3t² - 12t

<h3>Determine the values of t for which the particle is at rest </h3>

<u>First step : Determine the first derivative of eac equations</u>

dx = 3t² - 6t

dy = 6t² - 6t - 12

<u>Next step : </u><u>determine</u><u> the value of slope ( dy/dx ) = o </u>

dy / dx = ( 6 (t² - t - 2) )  /  ( 3t ( t - 2) )

Therefore

dy / dx = ( 2 ( t + 1 ) (t - 2) ) / ( t ( t -2) )

           = 0

Therefore at ; t = -1 and 2  the particle is at rest

Hence we can conclude that Neglecting the negative value the particle will be at rest when t = 2

Learn more about Object at rest : brainly.com/question/24160573

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<u>Attached below is the complete question</u>

<em>The position of a particle moving in the xy-plane is given by the parametric equations x = t3 - 3t2 and y = 2t3 - 3t2 - 12t. For what values of t is the particle at rest?</em>

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What is the maximum acceleration the belt can have without the crate slipping? express your answer using two significant figures
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If acceleration of the belt exceeds the value determined in the previous question, what is the acceleration of the crate?


In this situation, the kinetic friction force is causing the crate to decelerate. So the net force on the crate is 78.4 N minus the kinetic friction force.


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3 years ago
Tyler drives 50km north. Tyler then drives back 30km south. What distance did he cover? What was his displacement?
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Three wires meet at a junction. wire 1 has a current of 0.40 aa into the junction. the current of wire 2 is 0.73 aa out of the j
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The magnitude of the current in wire 3 is (I₃)= 0.33A

<h3>How to calculate the value of the magnitude of the current in wire 3 ?</h3>

To calculate the magnitude of the current in wire 3 we are using the Kirchhoff’s current law,

I₁ + I₂ + I₃ = 0

Where we are given,

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We have to calculate the magnitude of the current in wire 3, I₃

Now we put the known values in above equation, we get,

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