During the process of intersection, two bodies move in such a way that they coincide at the intersection position ($s$) and the intersection time ($t$).

For this to occur, each body must start from its initial position and time, with displacements of the first stage speed ($v_1$) and the first stage speed ($v_1$) respectively, such that the coincidence occurs.

mechanisms

In the case of interception, two bodies move in such a way that they will coincide at ERROR:10259.1 in their the intersection position ($s$).

For this purpose, each body:

• Starts at the initial time of first object ($t_1$) with the initial position of first object ($s_1$) as its initial position and the first stage speed ($v_1$) as its displacement.
• Starts at the initial time of second object ($t_2$) with the initial position of second object ($s_2$) as its initial position and the second stage speed ($v_2$) as its displacement.

These conditions must be met for the interception to occur.

This allows the diagrams of position over time to be coupled as shown in the following representation:

image

In the case of an intersection or collision between two objects, it's common that the first stage speed ($v_1$) and the second stage speed ($v_2$) must be such that coincidence occurs.

This means that the distance traveled by first object ($\Delta s_1$) and the travel time of first object ($\Delta t_1$) must result in a first stage speed ($v_1$),

equation=3152,1

such that with the distance traveled by the second object ($\Delta s_2$) and the travel time of second object ($\Delta t_2$), we obtain a second stage speed ($v_2$),

equation=3152,2

so that they ultimately coincide in time and space (position):

image

In the case of a movement where two objects intersect, such as the intersection position ($s$) and the intersection time ($t$), it is common for both. Therefore, if for the first object, the initial time of first object ($t_1$) and the initial position of first object ($s_1$) with the first stage speed ($v_1$) fulfill:

equation=3154,1

and for the second object, the initial time of second object ($t_2$) and the initial position of second object ($s_2$) with the second stage speed ($v_2$) fulfill:

equation=3154,2

which is represented as:

image

The key is that both objects meet at the intersection position ($s$) at time the intersection time ($t$). For this to happen, object 1 starts its journey at the initial position of first object ($s_1$) at ERROR:10252.1 with a velocity of ERROR:10238.1, while object 2 begins its journey at the initial position of second object ($s_2$) at ERROR:10253.1 with a velocity of ERROR:10239.1. During this process, object 1 travels ERROR:10254.1 at ERROR:10256.1, while object 2 travels ERROR:10255.1 at ERROR:10257.1:

model

We can calculate the distance traveled in a time ($\Delta s$) from the starting position ($s_0$) and the position ($s$) using the following equation:

kyon

We can calculate the distance traveled in a time ($\Delta s$) from the starting position ($s_0$) and the position ($s$) using the following equation:

kyon

To describe the motion of an object, we need to calculate the time elapsed ($\Delta t$). This magnitude is obtained by measuring the start Time ($t_0$) and the the time ($t$) of said motion. The duration is determined by subtracting the initial time from the final time:

kyon

To describe the motion of an object, we need to calculate the time elapsed ($\Delta t$). This magnitude is obtained by measuring the start Time ($t_0$) and the the time ($t$) of said motion. The duration is determined by subtracting the initial time from the final time:

kyon

The mean Speed ($\bar{v}$) can be calculated from the distance traveled in a time ($\Delta s$) and the time elapsed ($\Delta t$) using:

kyon

The mean Speed ($\bar{v}$) can be calculated from the distance traveled in a time ($\Delta s$) and the time elapsed ($\Delta t$) using:

kyon

If the speed is constant, the velocity will be equal to the initial Speed ($v_0$). In this case, the distance traveled as a function of time can be calculated using the difference between the position ($s$) and the starting position ($s_0$), divided by the difference between the time ($t$) and the start Time ($t_0$):

kyon

The corresponding equation defines a straight line in space-time.

If the speed is constant, the velocity will be equal to the initial Speed ($v_0$). In this case, the distance traveled as a function of time can be calculated using the difference between the position ($s$) and the starting position ($s_0$), divided by the difference between the time ($t$) and the start Time ($t_0$):

kyon

The corresponding equation defines a straight line in space-time.