Kinematics

Motion

The first change that is easy to observe is the change in the position of the body. That change is called motion. We'll try to find out what is common in all motions. We will limit ourselves only to describing the motion, without seeking the causes of motion. This past of mechanics is called kinematics. (picture - page 14)

Motion is a relative change in the body position in relation to the environment. The set of all points through which the body passes in his motion is called the path.

The uniform and uniformly accelerated motion along the straight line

At the uniform motion along the straight line the body passes in the equal periods of time the equal path. Here the real speed is equal to the average speed. At he uniformly accelerated motion along the straight line the body in the equal periods of time receives the equal growth of speed. Here the acceleration is a constant.

Free Fall

The most common and well known example of the motion with the constant acceleration is free fall. All the bodies in the free fall are under work of the constant force - gravitation. Since the quantity of gravitation is proportional to the mass of the body, than the constant acceleration will be constant and equal to all bodies. This simple fact was not easy to see: because of the friction of the air, the heavier bodies fall quicker than those with smaller mass. Only Galileo succeeded, with this experiment on the Tower of Pizza, to prove that heavy and light bodies fall at the same speed. The acceleration at free fall is approx. g= 9,81 m/s2 depending upon the geographic position and height above sea-level. (Table page 26. and photo - page 26).

The vector demonstration of motion

The importance of vector demonstration of kinematics quantities is most obvious when conforming the motion. Each motion can be decomposed into component straight line motions, then shown like vectors. In that each motion can be shown as the sum of all simple motions. The same rules that value for motion, are also applicable for path and for acceleration, since those two quantities can be derived from the vector quantities - path, by scalar dividing - time. According to that fact, we can talk about components of speed and acceleration. It is most common to show the components of motion in the direction of coordinate axes, or better to say, that suitable coordinate axes are chosen in the direction of the component motions. It is why we usually talk about o component of speed in the direction of axes x or y or z or in the radial direction.

The example of the complex motion: horizontal projection

The horizontal projection is in fact the complex motion which consists of two components:

-         uniform motion on the straight line (horizontal component H)

-         free fall (vertical component V)

-         the vertical component V is constantly changed in quantity, so we'll in fact observe very short segment dR resultant motion, which we'll be reached by vector sum of the component segments dH and dV. The equation of the horizontal projection will be reached through the equation of his components: x= v0t, y= -g/2*t2.