An athlete swims the length if 50m pool in 20s and makes the return trip to starting point in 22s.Determine the average speed and velocities a. the first half of the trip b.second half of the trip c. Round trip
To determine the average speed and velocities for different segments of the trip and the round trip, we need to use the formula:
Average Speed = Total Distance / Total Time
Average Velocity = Displacement / Total Time
First, let's calculate the total distance and total time for each segment:
a. First Half of the Trip:
Distance = 50 m
Time = 20 s
b. Second Half of the Trip:
Distance = 50 m
Time = 22 s
c. Round trip:
Distance = 50 m + 50 m = 100 m
Time = 20 s + 22 s = 42 s
Now, we can calculate the average speed and velocities:
a. Average speed for the first half of the trip:
Average Speed = Total Distance / Total Time
= 50 m / 20 s
= 2.5 m/s
Average Velocity = Displacement / Total Time
= 0 m (since the starting and ending points are the same) / 20 s
= 0 m/s
b. Average speed for the second half of the trip:
Average Speed = Total Distance / Total Time
= 50 m / 22 s
= 2.27 m/s (rounded to two decimal places)
Average Velocity = Displacement / Total Time
= 0 m (since the starting and ending points are the same) / 22 s
= 0 m/s
c. Average speed for the round trip:
Average Speed = Total Distance / Total Time
= 100 m / 42 s
≈ 2.38 m/s (rounded to two decimal places)
Average Velocity = Displacement / Total Time
= 0 m (since the starting and ending points are the same) / 42 s
= 0 m/s
So, the results are:
a. Average speed for the first half of the trip: 2.5 m/s
Average velocity for the first half of the trip: 0 m/s
b. Average speed for the second half of the trip: 2.27 m/s
Average velocity for the second half of the trip: 0 m/s
c. Average speed for the round trip: 2.38 m/s
Average velocity for the round trip: 0 m/s
To determine the average speed and velocities, we first need to understand the definitions of speed and velocity.
Speed is the distance traveled per unit of time, while velocity is the displacement traveled per unit of time. Displacement refers to the change in position of an object relative to its starting point.
a. First half of the trip:
The length of the pool is 50m. The athlete swims the length of the pool in 20s, which means the average speed for the first half of the trip is calculated by dividing the distance (50m) by the time (20s):
Average speed = Distance / Time = 50m / 20s = 2.5 m/s
Since the athlete swims directly back to the starting point, the displacement for the first half of the trip is zero. Therefore, the average velocity for the first half of the trip is also zero.
b. Second half of the trip:
The second half of the trip is the return trip from the end of the pool to the starting point. This distance is also 50m, but the athlete swims it in 22s. So, the average speed for the second half of the trip is calculated as:
Average speed = Distance / Time = 50m / 22s ≈ 2.27 m/s
Again, the athlete returns to the starting point, so the displacement for the second half of the trip is also zero. Therefore, the average velocity for the second half of the trip is also zero.
c. Round trip:
To determine the average speed for the round trip, we can calculate the total distance traveled and divide it by the total time taken.
Total distance = Distance of first half + Distance of second half = 50m + 50m = 100m
Total time = Time for the first half + Time for the second half = 20s + 22s = 42s
Average speed = Total distance / Total time = 100m / 42s ≈ 2.38 m/s
Since the athlete returns to the starting point, the displacement for the round trip is zero. Therefore, the average velocity for the round trip is also zero.
In summary:
a. First half of the trip: Average speed = 2.5 m/s, Average velocity = 0 m/s
b. Second half of the trip: Average speed = 2.27 m/s, Average velocity = 0 m/s
c. Round trip: Average speed = 2.38 m/s, Average velocity = 0 m/s
speed = distance/time
velocity = displacement/time
so, assuming the 1st half is in a positive direction,
(a) speed = 50/20 = 2.5 m/s
velocity = +50/20 = +2.5 m/s
and so on