Answer:
a) The total displacement is 180 km to the north.
b) The average velocity is 64 km/h due north.
c) The average speed is 64 km/h.
Step-by-step explanation:
Hi there!
a) The average velocity (av) is calculated as follows:
av = Δx / Δt
Where:
Δx = displacement (final position - initial position)
Δt = elapsed time.
First, let´s find the displacement in 35 min ((35/60) h) at 85 km/h:
av = Δx / Δt
85 km/h = Δx / ((35/60) h)
Δx = 85 km/h · (35/60) h
Δx = 50 km to the north
Then, the total displacement will be 50 km + 130 km = 180 km north
b) Now, let´s find the average velocity for the entire trip:
av = Δx / Δt
av = 180 km /(2 h + (15/60) h + (35/60) h)
av = 64 km/h
The average velocity is 64 km/h due north.
c) The speed is the magnitude of the velocity. It has no direction and is calculated as the traveled distance over time:
v = d/t
In this case, the distance is the same as the displacement because the motorist drives always north. Then, the average velocity will be equal to the average speed:
v = 180km/(2 h + (15/60) h + (35/60) h)
v = 64 km/h
What if the motorist drives the first 35 minutes due south and then 130 km due north?
In that case, the total displacement would be (130 km - 50 km) 80 km north from the starting point (we have considered north as the positive direction in our frame of reference). Then the average velocity will be less than the average speed:
av = displacement / time
av = 80 km / (2 h + (15/60) h + (35/60) h) = 28 km/h
While the average speed will be the same:
v = traveled distance / time
v = 180 km / (2 h + (15/60) h + (35/60) h) = 64 km/h