The average speed for a mobile particle it is defined as the ratio between the variation of the position that it experiences and the time interval used in the change. The simplest situation is one in which the particle moves along a straight line represented by the x-axis..
Suppose the moving object occupies positions x1 and xtwo in times t1 and youtwo respectively. The definition of average speed vm is represented mathematically like this:
The units of vm in International System they are meters / second (m / s). Other commonly used units that appear in texts and mobile devices are: km / h, cm / s, miles / h, feet / s and more, as long as they are of the form length / time.
The Greek letter "Δ" is read "delta" and is used to briefly indicate the difference between two quantities..
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Average velocity is a vector, since it is related to the change in position, which in turn is known as scroll vector.
This quality is represented in bold or by an arrow above the letter that designates the magnitude. However, in one dimension, the only possible direction is that of the x-axis and therefore the vector notation can be dispensed with.
Since vectors have magnitude, direction, and sense, an initial look at the equation indicates that the average velocity will have the same direction and sense as the displacement..
Let's imagine the particle in the example moving along a straight line. To describe its movement, it is necessary to indicate a reference point, which will be the "origin" and will be denoted as O.
The particle can move toward or away from O, either to the left or to the right. It can also take a long or little time to get to a certain position.
The magnitudes that have been mentioned: position, displacement, time interval and average speed, describe the behavior of the particle while it moves. It's about the magnitudes kinematics.
To distinguish the positions or locations to the left of O, the sign (-) is used and those to the right of O carry the sign (+).
The average speed has a geometric interpretation that can be seen in the following figure. It is the slope of the line that passes through points P and Q. When cutting the curve position vs. time at two points, it is a straight line drying.
For the following analysis it should be taken into account that ttwo > t1. That is, the next instant is always greater than the current one. In this way ttwo - t1 is always positive, which usually makes sense on a daily basis.
Then the sign of the mean velocity will be determined by that of xtwo - x1. Note that it is important to be clear about where point O -the origin- is, since this is the point with respect to which the particle is said to go "to the right" or "to the left".
Either "forward" or "backward", as the reader prefers.
If the mean velocity is positive it means that on average the value of "x”Increases over time, although this does not mean that it may have decreased at some point in the time period considered. - Δt -.
However in global terms, at the end of time Δt, she ended up with a bigger position than she had in the beginning. The details of the movement are ignored in this analysis..
What if the average velocity turns out to be negative? Then it means that the particle ends with a smaller coordinate than the one with which it started. Roughly he moved back. Let's look at some numerical examples:
Example 1: Given the start and end positions indicated, indicate the sign of the average speed. Where did the particle move globally?
a) x1 = 3 m; xtwo = 8 m
Answer: xtwo- x1 = 8 m - 3 m = 5 m. Positive mean velocity, particle moved forward.
b) x1 = 2 m; xtwo = -3 m
Answer: xtwo - x1 = -3 m - 2 m = -5 m. Negative mean velocity, the particle moved backwards.
c) x1 = - 5 m; xtwo = -12 m
Answer: xtwo - x1 = -12 m - (-5 m) = -7 m. Negative mean velocity, the particle moved backwards.
d) x1 = - 4 m; xtwo = 10 m
Answer: xtwo - x1 = 10 m - (-4m) = 14 m. Positive mean velocity, particle moved forward.
Can the average velocity be 0? Yes. As long as the starting point and the arrival point are the same. Does this mean that the particle was necessarily at rest the entire time??
No, it just means that the trip was roundtrip. Perhaps it traveled quickly or perhaps very slowly. For now it is not known.
This leads us to define a new term: medium speed. In Physics it is important to distinguish between vector quantities and non-vector quantities: scalars.
For the particle that made the round trip, the average velocity is 0, but it may or may not have been very fast. To find out, the mean speed is defined as:
The units for average speed are the same as those for average speed. The fundamental difference between both magnitudes is that the average velocity includes interesting information about the direction and sense of the particle..
On the other hand, the average speed provides only numerical information. With it you know how fast or slow the particle moved, but not if it moved forward or backward. So it is a scalar magnitude. How to distinguish them when denoting them? One way is by leaving the bold for the vectors, or by placing an arrow on them.
And it is important to note that the average speed does not have to be equal to the average speed. For the round trip the average speed is zero, but the average speed is not. Both have the same numerical value when always traveling in the same direction.
You drive back home from school leisurely at 95 km / h for 130 km. It starts to rain and slows down to 65 km / h. He finally gets home after driving for 3 hours and 20 minutes.
a) How far is your home from school?
b) What was the mean speed?
Answers:
a) Some preliminary calculations are necessary:
The trip is divided into two parts, the total distance is:
d = d1 + dtwo, with d1 = 130 km
t2 = 3.33 - 1.37 hours = 1.96 hours
Calculation of dtwo:
dtwo = 65 km / h x 1.96 h = 125.4 km.
The school is distant d1 + dtwo = 255.4 km from home.
b) Now we can find the mean speed:
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