A runner a distance of 200m due east in 90 sec and 300m due west in 120 sec.
Find:
A) displacement and distance
B) average velocity and average speed.
A) Displacement and Distance:
To find the displacement, we need to find the net distance and direction from the initial position to the final position. Since the runner is moving due east and then due west, we need to subtract the distance travelled west from the distance travelled east.
Distance travelled east = 200m
Distance travelled west = 300m
Net distance = 200m - 300m = -100m (negative sign indicates the displacement is in the opposite direction)
Therefore, the displacement is -100m to the west.
To find the distance, we add the magnitudes of the distances travelled east and west:
Distance = |200m| + |300m| = 200m + 300m = 500m
Therefore, the distance travelled is 500m.
B) Average Velocity and Average Speed:
Average velocity is the ratio of displacement to the time taken. Average speed is the ratio of distance to time.
Average velocity = displacement / time
Average velocity = -100m / (90s + 120s) = -100m / 210s = -0.48 m/s (west)
Average speed = distance / time
Average speed = 500m / (90s + 120s) = 500m / 210s = 2.38 m/s