Answer:
vavg = 0.37 m/s
Explanation:
- The average speed is just the relationship between the total distance traveled, and the total time required for that travel , as follows:
[tex]v_{avg} = \frac{\Delta x}{\Delta t} (1)[/tex]
- We know that for the first leg of the journey, the ant crawls at a constant speed of 0.24 m/s, moving 3.0 m.
- We can find the time required for this part, just applying the definition of average velocity, and solving for the time t (which we will call t₁), as follows:
[tex]t_{1} =\frac{x_{1}}{v_{1} } = \frac{3.0m}{0.24m/s} = 12.5 s (2)[/tex]
- From the givens, we know that the time for the second part is exactly the half of the value found in (2), so we can write the total time Δt as follows:
[tex]\Delta t = t_{1} + \frac{t_{1} }{2} = 12.5 s + 6.25 s = 18.75 s (3)[/tex]
- We also know that in the second leg of the journey, the ant traveled 4.0 m, which adds to the 3.0 m of the first part, making a total distance of 7.0 m.
- Per definition of average speed, we can write the following expression as in (1) replacing Δx and Δt by their values, as follows:
[tex]v_{avg} = \frac{\Delta x}{\Delta t} = \frac{7.0m}{18.75m} = 0.37 m/s (4)[/tex]
