Amotorist drives north for 35 minutes at 85 km/h and then stops for 15 minutes. he then
continues north, traveling 130 km in 2 hours.
a) what is his total displacement?
b) what is his average velocity?
(c) what is his average speed?

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.

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

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