A person is travelling 6 km (E) then 4 km (N) and finally 2 km (W). Calculate the average speed And velocity. Show your work
To calculate the average speed, we need to find the total distance traveled and the total time taken.
The total distance traveled can be found by adding the distances traveled in each direction:
6 km (E) + 4 km (N) + 2 km (W) = 12 km
Now, let's assume that the person takes a fixed amount of time for each leg of the journey, perhaps 1 hour for simplicity.
The total time taken will be the sum of the times taken for each leg of the journey:
1 hour + 1 hour + 1 hour = 3 hours
So, the average speed can be calculated by dividing the total distance traveled by the total time taken:
Average speed = Total distance / Total time = 12 km / 3 hours = 4 km/h
Therefore, the average speed of the person's journey is 4 km/h.
Now, let's calculate the velocity. Velocity is a vector quantity and takes into account both the speed and the direction of motion. To find the velocity, we need to determine the total displacement and the total time taken.
The total displacement is the straight-line distance from the starting point to the end point. We can find this using the Pythagorean theorem:
Displacement = √[(6 km)^2 + (4 km)^2] = √[36 km^2 + 16 km^2] = √52 km ≈ 7.21 km
Again, assuming it took 3 hours to complete the journey, the total time taken is 3 hours.
Now, we can calculate the velocity by dividing the total displacement by the total time taken:
Velocity = Total displacement / Total time = 7.21 km / 3 hours ≈ 2.40 km/h
Therefore, the velocity of the person's journey is approximately 2.40 km/h to the northeast.