Math requirements

• Coordinate systems (Euclid, polar, spherical)
• Operations with vectors
• Standard form of motion equations
• Derivatives, operations with derivatives, integrals

Topics

• Object, material point, space, position, displacement, path, speed, velocity, acceleration

We define an object's motion as a change of its position in space during some time interval. We also neglect the internal structure of a moving object, considering it as a dimensionless "material point".

If a motion occurs along a straight line in a chosen coordinate system, then it is called "priamolineno" in this system.

Let's start a straight-line motion in a 2-D Euclidian space. Each point in this space is described by a pair of (x,y) coordinates. The point's coordinates also define the radius vector r_vec, starting in the center of the coordinate system and ending in this point. A journey from point A(x0,y0) to point B(x1,y1) is described by the distance S between points A and B, by the trajectory (or path L) our object traveled, and by the time deltaT required for this travel. We also define the speed of travel along the motion path as a scalar value v=deltaL/deltaT, and the vector value of travel velocity between A and B as v_vec= S_vect/deltaT. As we can see the S_vect is the vector difference between radius vectors of points A and B, and thus v_vec= (r_b -r_a)/deltaT. With deltaT->0 v and v_vect become derivatives of path and distance with respect to time. These derivatives are called correspondingly instantaneous speed and velocity. and an instantaneous speed corresponds to a module of the instantaneous velocity. Similarly, if the velocity is changed with time, we can define a quantity called acceleration, which is the derivative of velocity with respect o time. The description of material point motion in a given coordinate system using its position, speed, and acceleration is called kinematics.

• Equations of motion with uniform speed along x axis:
  • $ v = dx/dt = const$, $a=dv/dt= d2x/dt^2 = 0t$
    • $ v = v_0$, (1.1); $ x = x_0+ v_0 \times t $, (1.2)
• Equations of motion with uniform acceleration along x axis:
  • $ v = dx/dt$, $a=dv/dt= d2x/dt^2 = const$
  • $ v = v_0 +a \times t $, (2.1); $x = x_{0} + v_{0} \times t \pm a\times t^{2}/2$, (2.2)
  • $v^2={v_0}^2+ 2 \times a \times (x-x_0)$, from ( 2.2 and 2.3)
• Relative movements
• Kinematics of curved movement, specifically on a circle