How Do You Calculate Angle and Velocity in Particle Motion Analysis?

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SUMMARY

The discussion focuses on calculating the position, velocity, and angle of a particle moving in an xy plane, defined by the position vector r=(2.00(t^3) -5t)î + (6.00 - 7.00(t^4))j. Participants are tasked with finding the resultant position R, the velocity V, and the angle between the positive x-axis and the tangent line at t=25 seconds. Key concepts include converting from rectangular to polar notation and understanding the relationship between position and velocity.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with particle motion equations
  • Knowledge of polar and rectangular coordinate systems
  • Basic differentiation techniques
NEXT STEPS
  • Learn how to differentiate position vectors to find velocity
  • Study the conversion from rectangular to polar coordinates
  • Explore the concept of tangential velocity in particle motion
  • Investigate the use of parametric equations in motion analysis
USEFUL FOR

Students in physics or engineering courses, educators teaching kinematics, and anyone interested in particle motion analysis and vector calculus.

Daretodaredar
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Homework Statement


the position "r" of a moving particle moving in an xy plane is given by r=(2.00(t^3) -5t)î+ (6.00-7.00(t^4) )j with r in meters and t in seconds. In unit notation calculate:
A) R
B) Velocity
C) R when t is 25 seconds
What is the able between the positive direction of the x-axis and a line tangent to its path at t=25 s


Homework Equations



I have no clue what to do!

The Attempt at a Solution

 
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Daretodaredar said:

Homework Statement


the position "r" of a moving particle moving in an xy plane is given by r=(2.00(t^3) -5t)î+ (6.00-7.00(t^4) )j with r in meters and t in seconds. In unit notation calculate:
A) R
B) Velocity
C) R when t is 25 seconds
What is the able between the positive direction of the x-axis and a line tangent to its path at t=25 s


Homework Equations



I have no clue what to do!

The Attempt at a Solution


Welcome to the PF.

What is "unit notation"?

And surely in the Relevant Equation section, you could list the method for converting from rectangular to polar notation, since you are asked to find an angle. And what is the relationship between the position R(t) and the velocity V(t) in general?

You need to show some effort on your schoolwork questions, if you want to receive tutorial help here.
 

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