The average acceleration tom is the magnitude that describes the variation of the speed of a particle in the course of time. It is important, because it shows the variations that the movement experiences.
To express this magnitude in mathematical terms, it is necessary to consider two speeds and two instants of time, which are respectively denoted as v1 and Vtwo, and you1 and youtwo.
Combining the values according to the definition offered, the following expression will be obtained:
In the international SI system the units for am will be m / stwo, although other units involving length per unit time squared will do.
For example, there is the km / h.s which is read "kilometer per hour and per second". Note that the unit of time appears twice. Thinking of a mobile moving along a straight line, it means that for every second elapsed, the mobile increases its speed by 1 km / h. Either it decreases it by 1 km / h for every second that passes.
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Although acceleration is associated with an increase in speed, the truth is that carefully observing the definition, it turns out that any change in speed implies the existence of an acceleration.
And speed doesn't necessarily always change in magnitude. It may happen that the mobile only changes direction and keeps its speed constant. Still there is a responsible acceleration of this change.
An example of this is a car that makes a curve with a constant speed of 60 km / h. The vehicle is subject to acceleration, which is responsible for changing the direction of speed so that the car follows the curve. The driver applies it using the steering wheel.
Such acceleration is directed towards the center of the curved path, to keep the car from going off it. It receives the name of acceleration radial or normal. If the radial acceleration were suddenly canceled, the car would no longer be able to keep going around the curve and would continue in a straight line.
A car traveling around a curve is an example of movement in two dimensions, whereas when it is going in a straight line, its movement is one-dimensional. In this case, the only effect acceleration has is to change the speed of the car..
This acceleration is called acceleration tangential. It is not exclusive to one-dimensional motion. The car going around the curve at 60 km / h could at the same time accelerate to 70 km / h while taking it. In this case, the driver needs to use both the steering wheel and the accelerator pedal..
If we consider a one-dimensional motion, the mean acceleration has a geometric interpretation similar to that of the mean velocity, as the slope of the secant line that intersects the curve at the points P and Q of the velocity vs. time graph..
This can be seen in the following figure:
Let's look at some examples to calculate the average acceleration in various situations:
I) At a certain instant in time, a mobile moving along a straight line has a speed of + 25 km / h and 120 seconds later it has another of -10 km / h. What was the mean acceleration?
Since the motion is one-dimensional, the vector notation can be dispensed with, in which case:
vor = +25 km / h = +6.94 m / s
vF = -10 km / h = - 2.78 m / s
Δt = 120 s
Whenever you have an exercise with mixed magnitudes like this, in which there are hours and seconds, it is necessary to pass all the values to the same units.
Being a one-dimensional movement, the vector notation has been dispensed with.
II) A cyclist travels east at a rate of 2.6 m / s and 5 minutes later goes south at 1.8 m / s. Find its average acceleration.
The movement not it is one-dimensional, therefore the vector notation is used. The unit vectors i Y j indicate the directions together with the following sign convention, facilitating the calculation:
vtwo = - 1.8 j m / s
v1 = + 2.6 i m / s
Δt = 5 minutes = 300 seconds
As always with average or average magnitudes, the information provided is global. They do not offer details of what happened to the mobile at each moment of time, however what they contribute is still valuable for the description of the movement.
By means of the signs of both speed and acceleration, it is possible to know whether a mobile moving on a straight line accelerates or slows down. In both situations the acceleration is present, since the velocity is changing.
Here are some interesting considerations regarding the signs of these two quantities:
It is usually thought that whenever it is a negative acceleration, the mobile is braking. This is true if the speed of the mobile is positive. But if it is negative, the speed is actually increasing.
As always when studying movement, think of special cases. For example, what happens when the average acceleration is zero? Does it mean that the mobile has always kept its speed constant??
The answer is no. The mobile could have varied its speed in the considered interval, but the initial and final speeds were the same. At the moment the details of what happened in the interval are unknown, since the average acceleration does not offer more information.
What if the average acceleration tom equals acceleration to at any point in the time interval? This is a very interesting situation called Uniformly Varied Rectilinear Motion or MRUV for short..
It means that the speed changes uniformly over time. Therefore the acceleration is constant. In nature there is such a movement, with which everyone is familiar: free fall.
It is a known fact that the earth attracts objects towards its center and that when one is released at a certain height, it experiences the acceleration of gravity, whose value is approximately constant and equal to 9.8 m / stwo close to the surface.
If air resistance does not intervene, the movement is vertical and is known as free fall. When the acceleration is constant and choosing t0 = 0, the mean acceleration equation becomes:
vF = v0 + at = gt (v0= 0)
Where a = g = 9.8 m / stwo
An object is dropped from sufficient height. Finding the velocity after 1.25 second.
vor = 0, since the object is dropped, then:
vF = gt = 9.8 x 1.25 m / s = 12.25 m / s, directed vertically towards the ground. (The vertical downward direction has been taken as positive).
As the object approaches the ground, its velocity increases by 9.8 m / s for each elapsed second. The mass of the object is not involved. Two different objects, dropped from the same height and at the same time, develop the same speed as they fall.
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