Answer :
(a) The average velocity for walking 68.6 m at a speed of 2.36 m/s and then running 68.6 m at a speed of 3.86 m/s is 3.11 m/s.
(b) The average velocity for walking for 1.00 min at a speed of 2.36 m/s and then running for 1.69 min at 3.86 m/s is 3.42 m/s.
To calculate average velocity, we divide the total displacement by the total time taken.
(a) In the first case, we have two segments: walking and running. The displacement for each segment is 68.6 m. The total displacement is therefore 2 × 68.6 m = 137.2 m.
The total time taken is the sum of the time spent walking and the time spent running. To find the time, we divide the distance by the respective speeds:
Time for walking = 68.6 m ÷ 2.36 m/s = 29.15 s
Time for running = 68.6 m ÷ 3.86 m/s = 17.79 s
The total time taken is 29.15 s + 17.79 s = 46.94 s.
Now we can calculate the average velocity:
Average velocity = Total displacement ÷ Total time taken
Average velocity = 137.2 m ÷ 46.94 s ≈ 3.11 m/s
(b) In the second case, the distances and speeds remain the same, but the time is given in minutes. We need to convert the minutes to seconds before performing the calculations.
Time for walking = 1.00 min × 60 s/min = 60 s
Time for running = 1.69 min × 60 s/min = 101.4 s
The total time taken is 60 s + 101.4 s = 161.4 s.
Now we can calculate the average velocity:
Average velocity = Total displacement ÷ Total time taken
Average velocity = 137.2 m ÷ 161.4 s ≈ 3.42 m/s
Therefore, the average velocities are approximately 3.11 m/s for case (a) and 3.42 m/s for case (b).
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