As you know, motion in classical physics is described by Newton’s second law. Thanks to this law, the concept of body acceleration is introduced. In this article, we consider the basic acceleration formulas in physics, which use the concepts of force, velocity and the path traveled by the body.
The concept of acceleration through Newton’s second law
If an external force F¯ acts on some physical body of mass m, then in the absence of other influences on it, we can write the following equality:
F¯ = m * a¯
Here a¯ is a vector quantity called linear acceleration. As can be seen from the formula, it is directly proportional to the external force F¯, since the mass of the body can be considered constant at speeds much lower than the propagation velocity of electromagnetic waves. In addition, the vector a¯ coincides in direction with F¯.
The above expression allows us to write the first acceleration formula in physics:
a¯ = F¯ / m or a = F / m
Here the second expression is written in scalar form.
Acceleration, speed and distance traveled
Another way to find linear acceleration a¯ is to study the process of body motion along a straight path. Such a movement is usually described by characteristics such as speed, time and distance traveled. In this case, acceleration is understood as the rate of change of the speed itself.
For the rectilinear movement of objects, the following formulas are valid in scalar form:
1) a M = dv / dt;
2) a cp = (v 2 -v 1 ) / (t 2 -t 1 );
3) a cp = 2 * S / t 2
The first expression is instantaneous acceleration; it is defined as the time derivative of speed.
The second formula allows you to calculate the average acceleration. Here we consider two states of a moving object: its speed at time v 1 at time t 1 and a similar value of v 2 at time t 2 . Time t 1 and t 2 is counted from some initial event. We note that the average acceleration characterizes in general this value in the considered time interval. Inside it, the value of instantaneous acceleration can vary and significantly differ from the average a cp .
The third acceleration formula in physics makes it possible to determine also a cp , but already through the path S passed. The formula is valid if the body started moving at zero speed, that is, when t = 0, v 0 = 0. This type of movement is called uniformly accelerated. His striking example is the fall of bodies in the gravitational field of our planet.
Circular motion uniform and acceleration
As was said, acceleration is a vector and, by definition, is a change in speed per unit time. In the case of uniform motion around the circumference, the velocity module does not change, but its vector constantly changes direction. This fact leads to the appearance of a specific type of acceleration, called the centripetal. It is directed to the center of the circle along which the body makes a movement, and is determined by the formula:
a c = v 2 / r, where r is the radius of the circle.
This acceleration formula in physics demonstrates that its value grows faster with increasing speed than with decreasing radius of curvature of the trajectory.
An example of the manifestation of a c is the movement of a car entering a turn.