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A motorist 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?

User Wemu
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1 Answer

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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

User Wayne Tanner
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