A car is traveling a road that includes two sides of an equilateral triangle with a constant speed s. What is the magnitude of the average velocity v of the car?
To find the magnitude of the average velocity of the car, we need to calculate the total distance traveled divided by the total time taken.
First, let's determine the total distance traveled by the car. The road includes two sides of an equilateral triangle. Since the triangle is equilateral, each side has the same length.
Let's denote the length of each side of the triangle as "d." The total distance traveled by the car can be calculated as 2d (since the car travels two sides of the triangle).
To find the value of "d," we can use some geometrical properties of an equilateral triangle. Since the triangle is equilateral, all angles are 60 degrees, and the sum of the angles within a triangle is 180 degrees.
Now, let's calculate the value of "d." Since one angle of the triangle is 60 degrees, the other two angles must also be 60 degrees each. The sum of the lengths of the three sides of the triangle is equal to the perimeter of the triangle, which is given by:
Perimeter = 3d = 2s
Simplifying the equation, we find:
d = 2s/3
Now that we have the value of "d," we can calculate the total distance traveled by the car:
Total Distance Traveled (D) = 2d = 2(2s/3) = 4s/3
Next, we need to determine the total time taken to travel this distance. Since the car is traveling at a constant speed (s), and the average velocity is the displacement divided by the time taken, the total time taken is equal to the total distance divided by the speed:
Total Time Taken (T) = D / s = (4s/3) / s = 4/3
Finally, we can calculate the magnitude of the average velocity by dividing the total distance traveled by the total time taken:
Magnitude of Average Velocity (v) = D / T = (4s/3) / (4/3) = s
Therefore, the magnitude of the average velocity of the car is s.