Motion is the basic state of the matter surrounding us. Acceleration is an important kinematic characteristic of any kind of mechanical motion. In this article, we consider what this physical quantity is and by what formula the average acceleration is calculated.
Where does the acceleration of bodies come from?
Before writing down and explaining the formula for average acceleration, let us consider where it comes from when bodies move and what this value is.
Newton’s first law states that the body does not change its rectilinear trajectory of motion and its speed if no external forces act on it. What happens if these forces begin to act? This question can be answered if we recall the second Newtonian law. We will write it in the form familiar to us:
F¯ = m * a¯
The action of the force F¯ on a body having mass m leads to the appearance of acceleration a¯. The last quantity is vectorial and is directed towards the acting force. According to this expression, acceleration is not related to the body velocity v¯, however, it is associated with a change in this speed.
Speed and formula of average acceleration in physics
The formula written above determines the dynamics of the motion of bodies. In this paragraph we will tell about his kinematics. According to the definition in physics, acceleration is a value that shows how fast the speed changes. Moreover, the change takes into account not only the module, but also the velocity vector. The formula for instant acceleration is written as follows:
a¯ = dv¯ / dt.
If the dependence of speed on time is known, then, taking its first derivative, we obtain an expression of the dependence of acceleration on time, that is, at any moment we can calculate the numerical value of a¯.
Instant acceleration is not of great practical importance, since in practice the global movements of bodies in space are important, and not their local kinematic characteristics at a given point of the trajectory. Therefore, average values are used to describe the motion process. The average acceleration shows how the speed has changed over the considered time interval Δt. The formula for the average acceleration is:
a cp ¯ = (v 2 ¯-v 1 ¯) / Δt or
a cp ¯ = Δv¯ / Δt, where Δv¯ = v 2 ¯-v 1 ¯
Here v 2 ¯, v 1 ¯ are the speeds at the final and initial time instants. For example, for uniform motion in a straight line, the velocity vector does not change, this means that the average acceleration will be zero. On the other hand, for uniform rotation, the velocity modulus is preserved, but its vector is constantly changing. The latter leads to the appearance of some average acceleration, which is called centripetal.
Free fall and acceleration
Everyone knows that due to the existence of gravity, all objects on our planet fall to its surface, if you throw them. During the free fall of bodies, the planet tells all of them the constant acceleration of free fall. To determine it, one should drop a body of some mass from a height h and measure the time t, during which the body will fall to the surface of the earth. The formula for the average acceleration of gravity g has the form:
g = 2 * h / t 2
The value of g changes by several percent when moving along the surface of the planet, since it depends on the distance to the center of the Earth, as well as on the local characteristics of the earth's crust. In addition, its value decreases with increasing height.