Acceleration is a familiar word. Not an engineer, it most often comes across in news articles and issues. Acceleration of development, cooperation and other social processes. The original meaning of this word is connected with physical phenomena. How to find the acceleration of a moving body, or acceleration as an indicator of the car's power? Can it have other meanings?
What happens between 0 and 100 (term definition)
Indicator of the power of the car is considered to be the time of its acceleration from zero to hundreds. But what happens in between? Consider our Lada Vesta with its claimed 11 seconds.
One of the formulas for how to find the acceleration is written as follows:
a=(V2 – V1) / t
In our case:
a – acceleration, m/s∙s
V1 – initial speed, m/s;
V2 – final speed, m/s;
t – time.
Let's bring the data to the SI system, namely km/h we will recalculate in m/s:
100 km/h=100000 m /3600 s=27.28 m/s.
Now you can find the acceleration of the Kalina:
a=(27, 28 – 0) / 11=2.53 m/s∙s
What do these numbers mean? An 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 a place (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 is 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, what is its primary source. There is only one answer - 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 a 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 – mass, kg;
a – acceleration, m/s∙s.
Referring to the product of the Russian car 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
Does this mean that if you do not release the gas pedal, the car will pick up speed until it reaches the speed of sound? 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 the acceleration at the time when the Lada "flies" at such a speed?
a=F / m=(Fwheels – Fresist.) / 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 the acceleration
First of all, in order to calculate the speed of any material body at the moment of interest, as well as its location.
Suppose that our "Lada Vesta" accelerates on the Moon, where there is no frontal air resistance due to its absence, then its acceleration at some stage will be stable. In this case, we determine the speed of the car 5 seconds after the start.
V=V0 + a ∙ t=0 + 2.53 ∙ 5=12.65 m/s
or 12.62 ∙ 3600 / 1000=45.54 km/h
V0 – initial point speed.
And how far from the start will our lunar car be at this moment? To do this, the easiest way is to use the universal formula for determining the coordinates:
x=x0 + V0t + (at2) / 2
x=0 + 0 ∙ 5 + (2.53 ∙ 52) / 2=31.63 m
x0 – initialpoint coordinate.
This is exactly the distance that Vesta will have time to leave 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 hits the moon, it will not be soon, its acceleration, in addition to the power of the new injection engine, is affected not only by air resistance.
At different speeds of the motor, it produces a different effort, this is not taking into account the number of the engaged gear, the coefficient of adhesion of the wheels to the road, the slope of this very road, wind speed and much more.
What other accelerations are there
Strength can do more than just make the body move forward in a straight line. For example, the force of gravity of the Earth causes the Moon to constantly curve its flight path in such a way that it always circles around us. Is there a force acting on the moon in this case? Yes, this is the same force that was discovered by Newton with the help of an apple - the force of attraction.
And the acceleration it gives to our natural satellite is called centripetal. How to find the acceleration of the Moon as it orbits?
aц=V2 / R=4π2R / T 2 where
ac – centripetal acceleration, m/s∙s;
V is the speed of the Moon in its orbit, m/s;
R – orbit radius, m;
T– the period of the Moon's revolution around the Earth, s.
ac=4 π2 384 399 000 / 23605912=0, 002723331 m/s∙s
