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 answer↓
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