In one of the important branches of physics — mechanics and its subsection — kinematics, the laws of motion of bodies are studied in the framework of Newton's classical theory. One of the important concepts of kinematics is the speed of movement of the body. The article considers the formulas for finding the speed.
The concept of speed
Before giving formulas for finding the speed for various types of motion, it is necessary to introduce the concept of speed itself. In physics, speed is understood as the speed with which the body changes its position in space. In SI, speed is measured in meters per second (m / s), but in practice other units of its measurement are often used, for example, kilometers per hour (km / h) or miles per hour (mph). When they say that a certain body moves along a certain trajectory at a speed of 10 m / s, it means that for every second this body travels a distance of 10 meters along a specified trajectory. Usually in tasks speed is denoted by the Latin letter v.
Uniform rectilinear movement
If the body moves in the forward direction, without turning anywhere, and without changing its speed, then they speak of its uniform and rectilinear motion. This is the simplest case of movement, which is almost never realized in practice, nevertheless it is useful to consider it within the framework of the issue under study.
In physics, the formula for finding the velocity for this type of motion is written as follows:
v = l / t,
where: t and l are the time of movement of the body and the path traveled by it during this time, respectively.
This formula follows directly from the definition of speed.
Equally accelerated rectilinear motion
This type of movement is already more complex than discussed in the paragraph above. Here we are talking about acceleration, which is a physical quantity that characterizes the change in speed.
For example, if the body increased its speed from 5 m / s to 10 m / s in 5 seconds, then its acceleration “a” will be equal to:
a = (10-5) / 5 = 1 m / s 2 ,
on the contrary, if the body reduced its speed from 10 m / s to 5 m / s in the same time, then the acceleration
a = (5-10) / 5 = -1 m / s 2 ,
that is, the negative sign of acceleration indicates that the body slows down its movement.
We consider two main cases of uniformly accelerated motion.
1. The body begins to move with constant acceleration. In this case, the initial velocity of the body is v 0 = 0, and the formula for finding the velocity at any time t takes the form:
v = a × t, where: a is the acceleration of motion.
2. The body was already moving with a certain initial speed v 0 , but then it began accelerated motion with acceleration a. In this case, for speed, you can write:
v = v 0 + a × t, whence it can be seen that the formula for finding the initial velocity will have the form:
v 0 = v - a × t,
where: v is the speed of the body at time t.
Problem solving example
Using the above formulas is quite simple.
We will solve a simple problem: let the car move at a certain speed, then start braking until it stops completely, which happened after 10 seconds. Knowing that during braking the car moved equally slowly with an acceleration of 3 m / s 2 , find its initial speed.
To solve the problem, we use the formula given in the previous paragraph:
v 0 = v - a × t.
Since the car stopped after t = 10 seconds, then its final speed is v = 0. Given that the car made equally slow motion, that is, a = - 3 m / s 2 , we can substitute all known values in the formula:
v 0 = v - a × t = 0 - (-3) × 10 = 30 m / s or in a more familiar form:
30 × 3600/1000 = 108 km / h.