Answer to Question #95718 in Classical Mechanics for Yaw

Question

How do I deduce the equation of displacement of a particle?

For example,
How was this equation, s=t^(2)+2t+4
made?

Answer 1

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

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