A car travels east 2 km for 5 minutes, then north 3 km for 8 minutes, and then west 4 km for 10 minutes. Determine the total distance traveled and the magnitude of displacement of the car. Also, what is the magnitude of the average velocity and the average speed?

#### Solution:

Show me the final answerâ†“

Let us draw out the travel path of the car to better visualize the question like so:

*Note that our origin is at A*

The total distance traveled by the car is:

To find the displacement, we can write a position vector from A to D and calculate it’s magnitude.

r_{magnitude}=\sqrt{(-2)^2+(3)^2}=3.6 km = 3600 m

To figure out the average velocity and speed, we need to first determine the length of time the car was in motion for.

The average velocity is displacement divided by time:

The average speed is total distance divided by the total time of travel:

#### Final Answers:

Displacement = 3.6 km = 3600 m

Average velocity = 2.61 m/s

Average speed = 6.52 m/s