Examples of how to calculate speed

Speed concept

In the field of Physics, the concept of “Speed” is defined as the vector magnitude – that is, it has a length and an orientation – by which the distance that an object or person travels in a given time is expressed.

It is universally expressed with the letter V capital, while its measurement is usually measured in meters per second, based on the International System of Units. It should also be clarified that this measure should never be confused with Acceleration.

To better explain this last point, it is necessary to clarify the speed refers to the rate of change of the position that has a specific object in a given unit of time, while acceleration refers to the rate of change that experiences the speed by unit of time.

Formula for calculating average vector speed

Clarifying the previous point, we then have that the universally recognized physical formula to calculate the speed at which a specific object travels a certain distance, is to divide that distance into the time it took to travel, having the velocity formula responds to the following equation:

Where “V” refers to speed; “d” at the distance traveled by the object in question and “t” the time this object took to travel that distance.

Formula for calculating vector speed on trajectory

However, this latter formula serves only to calculate what is known in Physics as the average vector velocity, that is, the velocity achieved by an object during a linear path. However, when the path or path followed by the object does not correspond to a line, but changed direction several times, it is said to be then a Medium Speed over Path, which has a different formula to be calculated.

In this sense, the universal formula for calculating the average speed on trajectory would be developed on the basis of dividing the sum of the distances of each vector by the total time spent by the object in traveling these distances, resulting in the next Equation:

In which “V” represents the speed; “d1”, “d2”, “d3” and “d4” are the distances that the object has traveled in each of the displacement vectors; and “t” is the total time spent by the object in traveling these distances.

Examples of how to calculate speed

Below we will give some examples of physical problems, where you should clear the Formula of Speed, having only two of the variants:

Exercise 1: A car covers a total of 172 km, between the city of Caracas and Valencia, taking a total of 3 hours. At what average speed did the car travel during its journey?

1.- To solve this exercise we must as a first step consider our formula, as well as specify the information with which it is counted, in order to identify what is the variable to clear.

2.- Then as a first step, we decide that the formula that we should use is the one that serves to calculate the average vector speed, because they tell us of a single distance. So we will use the following formula:

3.- Then we will proceed to see what data we have:

  • v=x
  • d=172 km
  • t=3 hours

4.- Having seen this, clearly “V” is the variable to be cleared. Then we will proceed to divide 172 km between three hours:

5.- We have then that the average speed of the car, during the route of 172 Km, in which it used 3 hours was 57.33 km/h. It should be clarified that while speed must be expressed in meters per second, this being its universal unit, it is sometimes expressed in higher measures such as Km/h to simplify its notation.

Exercise 2: A motorbike advances on the motorway at a speed of 80 km/h, for a total of 4 and a half hours. Calculate what the distance traveled by the bike was.

1.- As with the previous exercise, it is a question of calculating a variable circumscribed to the mean vector speed, as it is a straight-line offset. So the formula to be used will be:

2.- We must immediately check what data we have, so that we know what the variable will be to clear:

  • v= 80 km/h
  • d= x
  • t=4.5 h

3.- In this case, “d” is cleared, multiplying the variable “v” by the variable “t”. It means:

4.- Applying then the above formula we have to:

5.- In this way we have that the bike managed to travel a total of 360 km, at a speed of 80 km/h, for 4.5 h.

Exercise 3: A bus travels a total distance of 800 kilometers at an average speed of 70 km/h. How long did it take to complete the journey?

1.- As in the other two examples, having a single distance, we are faced with a calculation of average vector speed, so we will use the formula:

2.- We must also confront the information we have, in order to identify the variable to be cleared:

  •  v =70 km/h
  •  d=800 km
  •  t=x

3.- In this sense we have that the unknown to be cleared is “t”, which is calculated by dividing the distance “d” by the speed “v”, then obtaining the following formula:

4.- In this sense then we will proceed to calculate the unknown “t”:

5.- Having then that the bus took a total of 11.4 hours to travel 800 kilometers, at a speed of 70 km/h.

Examples of how to calculate speed
Source: Education  
September 18, 2019

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