A runner runs 2.9 km in 9 min and then takes 30 min to walk back to the starting point.
(a) What is the runner's average velocity for the first 9 min?
_______ km/h
(b) What is the average velocity for the time spent walking?
_______ km/h
(c) What is the average velocity for the whole trip?
_______ km/h
(d) What is the average speed for the whole trip?
_______ km/h
avgvelocity=distance/time
I will be happy to critique your thinking.
To find the average velocity, we need to divide the total distance traveled by the total time taken. Let's calculate each part separately for the given information:
(a) Average velocity for the first 9 min:
Distance covered = 2.9 km
Time taken = 9 min
To find average velocity, we need to convert minutes to hours:
(9 min) / (60 min/hour) = 0.15 hours
Average velocity = Distance covered / Time taken
Average velocity = 2.9 km / 0.15 hours
Average velocity = 19.33 km/h (rounded to two decimal places)
(b) Average velocity for the time spent walking:
Distance covered = 2.9 km (as the runner walked back to the starting point)
Time taken = 30 min
To find average velocity, we need to convert minutes to hours:
(30 min) / (60 min/hour) = 0.5 hours
Average velocity = Distance covered / Time taken
Average velocity = 2.9 km / 0.5 hours
Average velocity = 5.8 km/h
(c) Average velocity for the whole trip:
Total distance covered for the whole trip = distance covered during running and walking back = 2.9 km + 2.9 km = 5.8 km
Total time taken for the whole trip = time taken for running + time taken for walking = 9 min + 30 min = 39 min
To find average velocity, we need to convert minutes to hours:
(39 min) / (60 min/hour) = 0.65 hours
Average velocity = Total distance / Total time
Average velocity = 5.8 km / 0.65 hours
Average velocity = 8.92 km/h (rounded to two decimal places)
(d) Average speed for the whole trip:
Average speed is the total distance covered divided by the total time taken. Average speed does not consider direction.
Total distance covered for the whole trip = 2.9 km + 2.9 km = 5.8 km
Total time taken for the whole trip = 9 min + 30 min = 39 min
To find average speed, we need to convert minutes to hours:
(39 min) / (60 min/hour) = 0.65 hours
Average speed = Total distance / Total time
Average speed = 5.8 km / 0.65 hours
Average speed = 8.92 km/h (rounded to two decimal places)
Therefore, the answers are:
(a) The runner's average velocity for the first 9 min is 19.33 km/h.
(b) The average velocity for the time spent walking is 5.8 km/h.
(c) The average velocity for the whole trip is 8.92 km/h.
(d) The average speed for the whole trip is also 8.92 km/h.