A straight track is 1600 m in length. A runner begins at the starting line, runs due east for the full length of the track, turns around and runs halfway back. The time for this run is five minutes. What is the average velocity, and his average speed?
To find the average velocity, we need to calculate the displacement and divide it by the time taken. Displacement is a vector quantity, so we have to take into account both magnitude and direction.
The runner starts at the starting line and runs due east for the full length of the track, which means his displacement is +1600m (since east is considered positive). Then, he turns around and runs halfway back, so his displacement is -800m (since he is going in the opposite direction). The total displacement is then +1600m - 800m = +800m.
The time taken is given as 5 minutes.
Average velocity = Total displacement / Time taken = 800m / 5 min = 160 m/min, eastward.
Therefore, the average velocity is 160 m/min, eastward.
Average speed is a scalar quantity that only takes into account the magnitude of displacement. To find the average speed, we divide the total distance traveled by the time taken.
The runner runs the full length of the track (1600m) plus halfway back (800m), for a total distance of 2400m.
Average speed = Total distance / Time taken = 2400m / 5 min = 480 m/min.
Therefore, the average speed is 480 m/min.