Answer:
v = 79.3 km/h
Explanation:
- By definition, the average speed, is the quotient between the total distance traveled and the time needed to travel that distance.
- The total time, is the sum of three times: one while driving before stopping at the gas station (t₁), the time spent there (t₂) and the time since leaving the gas station until reaching the final destination (t₃) .
- Let's convert these times to seconds first:
[tex]t_{1} = 161 min* \frac{60s}{1min} = 9660 s (1)[/tex]
[tex]t_{2} = 23 min* \frac{60s}{1min} = 1380 s (2)[/tex]
[tex]t_{3} = 211 min* \frac{60s}{1min} = 12660 s (3)[/tex]
[tex]t_{tot} =t_{1} +t_{2} +t_{3} = 9660s + 1380s + 12660s = 23700s (4)[/tex]
- In order to find the total distance traveled, we need to add the distance traveled before stopping at the gas station (x₁) and the distance traveled after leaving it (x₂).
- Applying the definition of average speed, we can find these distances as follows:
[tex]x_{1} = v_{1} * t_{1} (5)[/tex]
[tex]x_{2} = v_{2} * t_{3} (6)[/tex]
- where v₁ = 107.0 km/h, and v₂= 67.0 km/h
- As we did with time, let's convert v₁ and v₂ to m/s:
[tex]v_{1} = 107.0 km/h*\frac{1000m}{1km}*\frac{1h}{3600s} = 29.7 m/s (7)[/tex]
[tex]v_{2} = 67.0 km/h*\frac{1000m}{1km}*\frac{1h}{3600s} = 18.6 m/s (8)[/tex]
- Replacing (7) and (1) in (5) we get x₁, as follows (in meters):
[tex]x_{1} = v_{1} * t_{1} = 29.7 m/s * 9660 s = 286902 m (9)[/tex]
- Doing the same for x₂ with (3) and (8):
[tex]x_{2} = v_{2} * t_{3} = 18.6 m/s * 12660 s = 235476 m (10)[/tex]
- Total distance traveled is just the sum of (9) and (10):
[tex]x_{tot} = x_{1} +x_{2} = 286902 m + 235476 m = 522378 m (11)[/tex]
- As we have already said, the average speed is just the quotient between (11) and (4), as follows:
[tex]v_{avg} =\frac{\Delta x}{\Delta t} = \frac{522378m}{23700s} = 22.0 m/s (12)[/tex]
[tex]v_{avg} = 22.0 m/s*\frac{1km}{1000m}*\frac{3600s}{1h} = 79.3 km/h (13)[/tex]
