When the mechanical motion of bodies in space is studied in physics, they always take into account the acceleration that occurs in this case. We consider in the article what acceleration is, and how it is indicated in physics, as well as solve the simple problem of calculating this quantity.
What is acceleration, and what are its types?
Acceleration is understood to mean the value, the meaning of which is the speed of change of the body speed. Mathematically, this definition is written as follows:
a = dv / dt.
If the function of the velocity time is known, then it is enough to find its first derivative in order to calculate the acceleration at a given time .
In physics, the letter of acceleration is lowercase Latin a. However, the so-called linear acceleration, which is measured in units of m / s 2 , is so designated. In addition to it, there is also angular acceleration. It shows the change in angular velocity and is expressed in units of rad / s 2 . This type of acceleration is denoted by the Greek lowercase letter Ξ± (alpha). Sometimes the letter Ξ΅ (epsilon) is used to designate it.
If the body moves along a trajectory curve, then the full acceleration decomposes into two components: tangential (determining the change in speed in magnitude) and normal (determining the change in speed in direction). These types of acceleration are also indicated by the letters a, but using the corresponding indices: a t and a n . Normal is often called centripetal, and tangential - tangent.
Finally, there is another type of acceleration that occurs when the bodies fall freely in the planetβs gravitational field. It is denoted by the letter g.
Acceleration physics problem
It is known that the body moves in a straight line. Its speed from time to time is determined by the following law:
v = 2 * t 2 -t + 4.
It is necessary to calculate the acceleration that the body will have at time t = 2.5 seconds.
Following the definition of a, we obtain:
a = dv / dt = 4 * t - 1.
That is, the value of a linearly depends on time. It is interesting to note that at the initial moment (t = 0) the acceleration was negative, that is, directed against the velocity vector. We get the answer to the problem by substituting t = 2.5 seconds into this equality: a = 9 m / s 2 .