Motion

MOTION

The mechanics is the relationship between force, matter and motion, we have to analyze mathematical methods describing the motion.
This part of mechanics called kinematics.

• Movement can be defined as a continuous change of position.

• In the real motion of an extended body, the various points of that move along different paths, but we will consider in principle a descriptionof motion in relation to a single (particle).

• Such a model is appropriate as long as there is no rotation or similar complications, or when the body is small enough to be considered as a point on the reference system.

• The simplest movement can be described is that of a point in a straight line, which will coincide with a coordinate axis.

DISPLACEMENT, SPEED AND ACCELERATION

Tounderstand how objects move when forces acting on them, understand the relationships between displacement, velocity and acceleration

Imagine a system consisting of three mutually perpendicular axes and a small body moving in the course of time, it describes some kind of trajectory in the coordinate space.

The principle, only the geometric aspects of the movement, whose study is called kinematicsand assume that somehow, the particle under study is limited to move only along the x-axis

Then you can describe his position at any time t by the distance x between the source and the particle, as there is a well-defined value of x associated with each time value t, x is a function of t.


For the foregoing will be possible to plot the displacement x versus time and get a chart like thefollowing.

Moving an object moving on the x axis plotted versus time. The amount ∆x/∆t represents the average speed in the time interval ∆t, while the limit of this amount when ∆t tends to zero, which is the derivative dx/dt, represents the instantaneous velocity at time t.

The average speed during a time interval t could be obtained given the distance that the particle in that interval,and noting that


(1)

is the tangent of the angle θ, it also represents the slope of the secant PQ joining the two points on the curve corresponding to time t and the displacement x + .

The instantaneous velocity can be considered as the slope of the tangent at P to the curve in Fig.
It is clearthat as ∆t y ∆x tend to zero in the limit, the slope of the secant PQ approaches the slope of the tangent to the curve at P.
From equation (2), one can consider that the instantaneous velocity Vx is the speed of change of displacement.
So if the instantaneous velocity is constant, then the average velocity is a time interval equal to the instantaneous velocity.
If the instantaneous velocity wasnot constant, then the speed depends on the chosen time interval and, in general, not be equal to the instantaneous velocity at the beginning or end of range.
You can also speak of the average acceleration āx for a certain interval, as the change in the instantaneous velocity experienced by the particle during one divided by the duration,.. ; so,(3)


Consequently, one can say that the instantaneous acceleration is the rate of change of instantaneous speed.



AVERAGE SPEED, INSTANTANEOUS AND SPEED

The average velocity of a particle is defined as the ratio of total distance and total time it takes to travel that distance:

Total distance
Average Speed = ————————Total time

The IS unit of the average speed, as speed, it is meters per second.
However, unlike the average speed, average speed has no direction, therefore carries no algebraic sign.
Knowing the average velocity of a particle does not provide any information about the travel details.
For example, suppose you take 8.0 hours to travel 280 km on your car. The average speed of the trip is...