Answer:
The average speed is 2.67 m/s
Explanation:
Constant Speed Motion
The speed of a moving object can be calculated as:
[tex]\displaystyle v=\frac{x}{t}[/tex]
Where
x = distance
t = time
Solving for t:
[tex]\displaystyle t=\frac{x}{v}[/tex]
The average speed is calculated as:
[tex]\displaystyle \bar v=\frac{x_t}{t_t}[/tex]
Where xt and tt are the total distance and time respectively.
The person walks at a constant speed of v1=2 m/s for a distance x. They take a time t1 to travel calculated by:
[tex]\displaystyle t_1=\frac{x}{v_1}[/tex]
Then, the person walks back at v2=4 m/s the same distance x. Thus, the second time is:
[tex]\displaystyle t_2=\frac{x}{v_2}[/tex]
The total time taken for the entire travel is:
[tex]\displaystyle t_t=\frac{x}{v_1}+\frac{x}{v_2}[/tex]
Simplifying and substituting:
[tex]\displaystyle t_t=\frac{x}{2}+\frac{x}{4}[/tex]
[tex]\displaystyle t_t=\frac{2x}{4}+\frac{x}{4}[/tex]
[tex]\displaystyle t_t=\frac{3x}{4}[/tex]
The total distance is xt=2x, thus the average speed is:
[tex]\displaystyle \bar v=\frac{2x}{\frac{3x}{4}}[/tex]
Simplifying:
[tex]\displaystyle \bar v=\frac{8}{3}=2.67[/tex]
The average speed is 2.67 m/s
