A runner cover a distance of 200m due east in 90 sec and 300m due west in 120 sec.
Find: a) displacement + distance
b) average speed + average velocity
a) Displacement:
To find the displacement, we need to determine the final position of the runner relative to the starting point. Since the runner first moves 200m east and then 300m west, the net displacement can be found by subtracting the distance moved west from the distance moved east.
Net displacement = 200m - 300m
Net displacement = -100m
Distance:
To find the total distance covered by the runner, we simply add the distances moved in each direction.
Total distance = 200m + 300m
Total distance = 500m
b) Average speed:
Average speed is calculated by dividing the total distance traveled by the total time taken.
Average speed = Total distance / Total time
Average speed = 500m / (90sec + 120sec)
Average speed = 500m / 210 sec
Average speed ≈ 2.38 m/s
Average velocity:
Average velocity is the displacement divided by the total time taken.
Average velocity = Displacement / Total time
Average velocity = -100m / (90sec + 120sec)
Average velocity = -100m / 210 sec
Average velocity ≈ -0.48 m/s
Therefore:
a) Displacement: -100m
Distance: 500m
b) Average speed: 2.38 m/s
Average velocity: -0.48 m/s