Answer to Question #95718 in Classical Mechanics for Yaw

Question #95718
How do I deduce the equation of displacement of a particle?

For example,
How was this equation, s=t^(2)+2t+4
made?
1
Expert's answer
2019-10-02T10:01:53-0400

First it is necessary to establish a reference system which consists of a Cartesian coordinate system.





The displacement equation is given by a general formula.


"S=S_{o}+V_{o}*t+\\frac{1}{2}a*t^{2}"


  • Where each term has a meaning.


The initial position is given by: "S_{o}" it is the position of the object at t = 0


The initial velocity is given by: "V_{o}"


  • If initially the object moves in the + x direction the velocity is positive.
  • If initially the object moves in the -x direction the velocity is negative.


Acceleration is given by: "a"



  • If the object is increasing velocity in the + X direction then the acceleration is positive
  • If the object is decreasing velocity in the -x direction then the acceleration is negative.


The time is given by:"t"


Example.

#one

A car leaves from rest at 3 meters from the origin and increases its velocity at a rate of 10m / s2, the position equation is given by:


In this case:

  • The initial position is:"S_{o}=3m"
  • The initial velocity is: '' Start from rest ''"V_{o}=0\\frac{m}{s}"
  • The acceleration is a"a=+10\\frac{m}{s^{2}}"
  • Time "t"


Expression for the position."S=S_{o}+V_{o}t +\\frac{1}{2}at^{2}\\text{ The units are omitted to facilitate the work }"

"S=3+0t +\\frac{1}{2}10t^{2} \\\\ S=3+\\frac{10}{2}t^{2} \\\\S=3+5t^{2} \\\\ \\text{ Organizing } \\boxed{S=5t^{2}+3}"



#2

A car initially travels at 30m / s when it applies the brakes and decreases its velocity at a rate of 4m / s2.


Where:

  • The Initial velocity is: "V_{o}=30\\frac{m}{s}"
  • The initial position "S_{o}=0m" (if not given, it is assumed that the origin is where the cell phone is initially)
  • Acceleration a"a=-4\\frac{m}{s^{2}}"
  • Time "t"


Expression for the position."S=S_{o}+V_{o}t +\\frac{1}{2}at^{2}\\text{ The units are omitted to facilitate the work }"

"S=0+30t -\\frac{1}{2}4t^{2} \\\\ S=30t-\\frac{4}{2}t^{2} \\\\S=30t+2t^{2} \\\\ \\text{ Organizing } \\boxed{S=2t^{2}+30t}"



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