a hiker travels north at 200m/s north and then turns and travels 200 m/s south. what is:

a) the average speed
b) the average velocity
c) the magnitude and direction in change in velocity

To find the average speed, you need to calculate the total distance traveled divided by the total time taken. In this case, the hiker traveled north at 200 m/s and then south at 200 m/s.

a) Average Speed: The hiker traveled 200 meters north and 200 meters south. Since the speed is given in meters per second, we can assume the time taken is the same for both directions. Therefore, the total distance traveled is 200 + 200 = 400 meters. To calculate the average speed, divide the total distance by the total time taken:

Average Speed = Total Distance / Total Time

Since the time taken is the same for both north and south, the average speed would be:

Average Speed = 400 meters / time

To find the exact value of the average speed, we need the value of time.

b) Average Velocity: Velocity is different from speed as it includes the direction of motion. To calculate average velocity, we need to find the total displacement divided by the total time taken.

The hiker traveled 200 meters north and then 200 meters south. Since the displacement includes direction, we consider the value as its difference:

Total Displacement = (200 meters north) - (200 meters south)
Total Time = time taken for north + time taken for south

If we assume the time taken for north and south is the same, the displacement would be zero, and the time taken would be the double of the time taken for either north or south. In this case, the average velocity would be:

Average Velocity = Total Displacement / Total Time
= 0 / (2 * time)

The average velocity would be zero since the displacement is zero.

c) Magnitude and Direction of Change in Velocity: The change in velocity is the difference between the final velocity and the initial velocity. In this case, the initial velocity is 200 m/s north, and the final velocity is 200 m/s south.

Magnitude of Change in Velocity = |final velocity - initial velocity|
= |(-200 m/s north) - (200 m/s south)|
= 400 m/s

Direction of Change in Velocity: The direction of change in velocity can be stated as south since the final velocity has a southward direction.