- Acceleration, speed and speed
- How Average Acceleration Is Calculated
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- Exercise resolved
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- References
The average acceleration at m is the magnitude that describes the variation of the velocity 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 v 1 and v 2, and t 1 and t 2.
Average acceleration is a very important kinematic parameter. Source: Pixabay.
Combining the values according to the definition offered, the following expression will be obtained:
In the SI international system the units for a m will be m / s 2, although other units involving length per unit time squared will do.
For example, there is the km / h which reads "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. Or it decreases it by 1 km / h for every second that passes.
Acceleration, speed and speed
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 radial or normal acceleration. If the radial acceleration were suddenly canceled, the car could no longer keep going around the curve and would continue in a straight line.
A car traveling around a curve is an example of motion in two dimensions, whereas when it is traveling in a straight line, its motion is one-dimensional. In this case, the only effect acceleration has is to change the speed of the car.
This acceleration is called tangential acceleration. 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 movement, the mean acceleration has a geometric interpretation similar to that of the mean speed, as the slope of the secant line that intersects the curve at the points P and Q of the speed vs. time graph.
This can be seen in the following figure:
Geometric interpretation of the mean acceleration. Source: Source: す じ に く シ チ ュ ー.
How Average Acceleration Is Calculated
Let's look at some examples to calculate the average acceleration in various situations:
I) At a certain instant of 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 average acceleration?
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Since the motion is one-dimensional, the vector notation can be dispensed with, in which case:
v o = +25 km / h = +6.94 m / s
v f = -10 km / h = - 2.78 m / s
Δt = 120 s
Whenever you have an exercise with mixed magnitudes like this one, in which there are hours and seconds, it is necessary to pass all the values to the same units.
As it is a one-dimensional movement, 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.
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The movement is not one-dimensional, therefore vector notation is used. The unit vectors i and j indicate the directions together with the following sign convention, facilitating the calculation:
- North: + j
- South: - j
- East: + i
- West: - i
v 2 = - 1.8 j m / s
v 1 = + 2.6 i m / s
Δt = 5 minutes = 300 seconds
v f = v 0 + at = gt (v 0 = 0)
Where a = g = 9.8 m / s 2
Exercise resolved
An object is dropped from sufficient height. Find the velocity after 1.25 second.
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v o = 0, since the object is dropped, then:
v f = 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.
References
- Giancoli, D. Physics. Principles with Applications. Sixth Edition. Prentice Hall. 21- 35.
- Resnick, R. (1999). Physical. Volume 1. Third edition in Spanish. Mexico. Compañía Editorial Continental SA de CV 20-34.
- Serway, R., Jewett, J. (2008). Physics for Science and Engineering. Volume 1. 7 ma. Edition. Mexico. Cengage Learning Editors. 21-39.