2d Motion, calculating time when v=0 from position vector

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SUMMARY

The discussion focuses on calculating the time at which the velocity of a particle, defined by the position vector r = ihat(2t^3 - 21t^2 + 60t + 10) + jhat(3/2)(t^2 - 10t + 9), is zero. The velocity vector is derived by taking the derivative of the position vector, resulting in v = (6t^2 - 42t + 60)ihat + (3t^2 - 15)jhat. To find when the particle is instantaneously at rest, both components of the velocity vector must be set to zero simultaneously, leading to two separate equations that must be solved together.

PREREQUISITES
  • Understanding of vector calculus, specifically derivatives of position vectors.
  • Familiarity with the concepts of velocity and instantaneous rest in physics.
  • Knowledge of solving polynomial equations.
  • Basic proficiency in using mathematical notation for vectors (i.e., ihat and jhat).
NEXT STEPS
  • Learn how to derive velocity vectors from position vectors in physics.
  • Study methods for solving simultaneous equations, particularly in the context of polynomial functions.
  • Explore the implications of setting vector components to zero in motion analysis.
  • Review examples of 2D motion problems involving position and velocity vectors.
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Students studying physics, particularly those focusing on mechanics and motion analysis, as well as educators looking for examples of vector calculus applications in real-world scenarios.

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Homework Statement


The position vector of a particle is given by r= ihat(2t^3-21t^2+60t+10) +jhat(3/2)(t^2-10t+9)
At what time, if any, is the velocity of the particle zero (ie what time is the particle instantaneously at rest)



Homework Equations





The Attempt at a Solution


Finding the velocity vector is simple, just taking the derivative of position
However, when I set that to 0 I have the ihat and the jhat and I don't know how to combine them to solve for the time. Is this even the right step?

If I take
v= (6t^2-42t+60)ihat+(3t^2-15)jhat
and set that to 0
how do I account for the vx and vy when setting that to 0?
Do I set vx and vy to 0 separately?

I'm really confused.

Thanks.
 
Physics news on Phys.org
In order for v to be zero, both components must be zero. (at the same time, of course)
 

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