an athlete leaves one end of a pool pf length l at t=0 and arrives at the other end at the time t1. she swim back and arrived at the starting position at the time t2. if she is swimming initially in the position x direction. determine her average velocities symbolically in (a) the first half of the swim. (b) the second half of the swim and (c) the round trip (d) what is her average speed for the round trip?
To determine an athlete's average velocities, we need to find the displacement and the total time taken for each section of the swim.
Let's consider the given information:
- The length of the pool is l.
- The athlete leaves one end of the pool at t=0 and arrives at the other end at time t1.
- She swims back and arrives at the starting position at time t2.
Now, let's find the average velocities for each section:
(a) First half of the swim:
The athlete travels from one end to the other end of the pool in the first half of the swim. The displacement in this case is the length of the pool, l. The time taken is t1.
Average velocity in the first half = displacement / time = l / t1.
(b) Second half of the swim:
The athlete swims back from the other end to the starting position in the second half of the swim. The displacement is also the length of the pool, l (since she returns to the starting position). The time taken is t2 - t1.
Average velocity in the second half = displacement / time = l / (t2 - t1).
(c) Round trip:
For the round trip, we consider both halves of the swim together. The displacement is zero since she returns to the starting position. The time taken is t2.
Average velocity for the round trip = displacement / time = 0 / t2 = 0.
(d) Average speed for the round trip:
The average speed is the total distance traveled divided by the total time taken. For the round trip, the total distance is twice the length of the pool (since she swims from one end to the other and then back to the starting position). The total time is t2.
Average speed for the round trip = total distance / total time = 2l / t2.
Therefore, the symbolically represented average velocities are:
(a) Average velocity in the first half = l / t1.
(b) Average velocity in the second half = l / (t2 - t1).
(c) Average velocity for the round trip = 0.
(d) Average speed for the round trip = 2l / t2.