How to find acceleration and what acceleration will help determine

Acceleration is a familiar word. Not an engineer, it most often comes across in news articles and issues. Acceleration of development, cooperation, other social processes. The original meaning of this word is associated with physical phenomena. How to find the acceleration of a moving body, or acceleration, as an indicator of the power of a car? But can it have other meanings?

What happens between 0 and 100 (definition of the term)

The car’s power indicator is considered to be the time of its acceleration from zero to hundreds. But what happens in the gap? Consider our “Lada Vesta” with its declared 11 seconds.

One of the formulas for finding acceleration is written as follows:

a = (V ₂ - V ₁ ) / t

In our case:

a - acceleration, m / s ∙ s

V1 - initial velocity, m / s;

V2 is the final velocity, m / s;

t is time.

We present the data in the SI system, namely, km / h will be converted to m / s:

100 km / h = 100,000 m / 3600 s = 27.28 m / s.

Now you can find the acceleration of the movement "Kalina":

a = (27.28 - 0) / 11 = 2.53 m / s ∙ s

What do these numbers mean? The acceleration of 2.53 meters per second per second indicates that for every second the speed of the "car" increases by 2.53 m / s.

When starting from scratch (from scratch):

• in the first second the car will accelerate to a speed of 2.53 m / s;
• for the second - up to 5.06 m / s;
• by the end of the third second, the speed will be 7.59 m / s, etc.

Thus, we can summarize: acceleration - an increase in the speed of a point per unit of time.

Newton’s second law, it’s easy

So, the acceleration value is calculated. It’s time to ask where this acceleration comes from, which is its primary source. The only answer is strength. It is the force with which the wheels push the car forward that causes it to accelerate. And how to find the acceleration, if the magnitude of this force is known? The relationship between these two quantities and the mass of the material point was established by Isaac Newton (this did not happen on the day when an apple fell on his head, then he discovered another physical law).

And this law is written like this:

F = m ∙ a, where

F - force, N;

m is the mass, kg;

a - acceleration, m / s ∙ s.

With regard to the product of the Russian automobile industry, you can calculate the force with which the wheels push the car forward.

F = m ∙ a = 1585 kg ∙ 2.53 m / s ∙ s = 4010 N

or 4010 / 9.8 = 409 kg ∙ s

This means that if you do not release the gas pedal, the car will gain speed until the speed of sound is reached? Of course not. Even when it reaches a speed of 70 km / h (19.44 m / s), the air drag reaches 2000 N.

How to find acceleration at a time when Lada "flies" at this speed?

a = F / m = (F _wheels - F _rds .) / m = (4010 - 2000) / 1585 = 1.27 m / s ∙ s

As you can see, the formula allows you to find both acceleration, knowing the force with which the engines act on the mechanism (other forces: wind, water flow, weight, etc.), and vice versa.

Why you need to know acceleration

First of all, in order to calculate the speed of a material body at an interesting moment in time, as well as its location.

Suppose that our Lada Vesta accelerates on the Moon, where there is no frontal resistance of air due to the lack thereof, then its acceleration at some stage will be stable. In this case, we determine the speed of the machine 5 seconds after the start.

V = V ₀ + a ∙ t = 0 + 2.53 ∙ 5 = 12.65 m / s

or 12.62 ∙ 3600/1000 = 45.54 km / h

V ₀ is the initial velocity of the point.

And at what moment will our lunar car be at this moment? To do this, it is easiest to use the universal formula for determining the coordinate:

x = x ₀ + V ₀ t + (at ² ) / 2

x = 0 + 0 ∙ 5 + (2.53 ∙ 5 ² ) / 2 = 31.63 m

x ₀ is the initial coordinate of the point.

It is at this distance that Vesta will be able to retire from the start line in 5 seconds.

But in fact, in order to find the speed and acceleration of a point at a given point in time, in reality it is necessary to take into account and calculate many other factors. Of course, if the Lada Vesta gets to the Moon, it will not be soon, its acceleration, besides the power of the new injection engine, is affected not only by air resistance.

At different revolutions of the motor, it gives out different forces, this still does not take into account the number of the gear engaged, the coefficient of adhesion of the wheels to the road, the slope of this same road, wind speed and much more.

What other accelerations are there

Strength can not only make the body move forward in a straight line. For example, the Earth’s gravitational force causes the Moon to constantly bend its flight path in such a way that it always circles around us. In this case, the moon is affected by force? Yes, this is the same force that Newton discovered with the help of an apple - the force of gravity.

And the acceleration that it gives to our natural satellite is called centripetal. How to find the acceleration of the moon when it moves in orbit?

a _C = V ² / R = 4π ² R / T ² , where

a _c - centripetal acceleration, m / s ∙ s;

V is the speed of the moon in orbit, m / s;

R is the radius of the orbit, m;

T– period of revolution of the Moon around the Earth, p.

a _c = 4 π ² 384 399 000/2360591 ² = 0.002723331 m / s ∙ s