The motion of bodies in space is described by a set of characteristics, among which the main ones are the distance traveled, speed and acceleration. The latter characteristic largely determines the peculiarity and type of movement itself. In this article, we consider the question that this is acceleration in physics, and we give an example of solving the problem using this value.
The main equation of dynamics
Before defining acceleration in physics, we give the main equation of dynamics, which is called the second Newtonian law. It is often written as follows:
F¯ * dt = dp¯
That is, the force F¯, which has an external character, exerted an effect on some body during the time dt, which led to a change in the momentum by the value dp¯. The left side of the equation is called the momentum of the body. We note that the quantities F¯ and dp¯ are of a vector nature, and the corresponding vectors are directed identically.
Each student knows the formula for the amount of movement, it is written like this:
p¯ = m * v¯
The quantity p¯ characterizes the kinetic energy stored in the body (velocity multiplier v¯), which depends on the inertial properties of the body (mass factor m).
If this expression is substituted into the formula of Newton’s 2nd law, then we obtain the following equality:
F¯ * dt = m * dv¯;
F¯ = m * dv¯ / dt;
F¯ = m * a¯, where a¯ = dv¯ / dt.
The introduced quantity a¯ is called acceleration.
What is acceleration in physics?
Now let us explain what the quantity a¯ introduced in the previous paragraph means. Let us write again its mathematical definition:
a¯ = dv¯ / dt
Using the formula, one can easily understand that this is acceleration in physics. The physical quantity a¯ shows how quickly the speed will change over time, that is, it is a measure of the speed of change of the speed itself. For example, in accordance with Newton’s law, if a force of 1 Newton acts on a body weighing 1 kilogram, it will acquire an acceleration of 1 m / s 2 , that is, for every second of movement the body will increase its speed by 1 meter per second.
Acceleration and speed
In physics, these are two different quantities that are interconnected by kinematic equations of motion. Both quantities are vectorial, but in the general case they are directed differently. Acceleration is always directed along the direction of the acting force. The speed is directed along the trajectory of the body. The vectors of acceleration and velocity will coincide with each other only when the external force in the direction of action coincides with the movement of the body.
Unlike speed, acceleration can be a negative value. The latter fact means that it is directed against the movement of the body and seeks to reduce its speed, that is, the process of inhibition occurs.
The general formula that links the speed and acceleration modules looks like this:
v = v 0 + a * t
This is one of the basic equations of rectilinear uniformly accelerated movement of bodies. It shows that over time, the speed increases linearly. If the motion is equally slow, then the minus should be put in front of the term a * t. The value of v 0 here is a certain initial velocity.
With uniformly accelerated (equally slow) movement, the following formula is also valid:
a¯ = Δv¯ / Δt
It differs from a similar expression in differential form in that here the acceleration is calculated over a finite period of time Δt. This acceleration is called the average over the marked time period.
Path and acceleration
If the body moves uniformly and in a straight line, then the path traveled by it in time t can be calculated as follows:
S = v * t
If v ≠ const, then the acceleration should be taken into account when calculating the distance traveled by the body. The corresponding formula is:
S = v 0 * t + a * t 2/2
This equation describes uniformly accelerated motion (for an equally slow motion, the + sign must be replaced by a - sign).
Circular motion and acceleration
It was said above that acceleration in physics is a vector quantity, that is, its change is possible both in direction and in modulus. In the case of the considered rectilinear accelerated motion, the direction of the vector a¯ and its modulus remain unchanged. If the module begins to change, then such a movement will no longer be uniformly accelerated, but will remain straightforward. If the direction of the vector a¯ begins to change, then the motion will become curved. One of the common types of such movement is the movement of a material point around a circle.
Two formulas are valid for this type of motion:
α¯ = dω¯ / dt;
a c = v 2 / r
The first expression is angular acceleration. Its physical meaning is the rate of change of angular velocity. In other words, α shows how quickly the body spins or slows down its rotation. The quantity α is tangential acceleration, that is , it is directed along the tangent to the circle.
The second expression describes the centripetal acceleration a c . If the linear speed of rotation remains constant (v = const), then the modulus a c does not change, however, its direction always changes and tends to direct the body to the center of the circle. Here r is the radius of rotation of the body.
Body free fall challenge
We found out that this is acceleration in physics. Now we show how to use the above formulas for rectilinear motion.
One of the typical problems are physics with acceleration of gravity. This value is the acceleration that the gravitational force of our planet tells all bodies with finite mass. In physics, the acceleration of gravity near the surface of the Earth is 9.81 m / s 2 .
Suppose some body was at a height of 20 meters. Then he was released. After how long will it be on the surface of the earth?
Since the initial speed v 0 is zero, then for the distance traveled (height h), we can write the equation:
h = g * t 2/2
Where do we get the fall time from:
t = √ (2 * h / g)
Substituting the data from the condition, we find that the body will be on earth in 2.02 seconds. In fact, this time will be slightly longer due to the presence of air resistance.