An athlete leaves one end of a pool of length L at t=0 S and...

$\mathrm{An}$ athlete leaves one end of a pool of length $L$ at $t=0$ S and arrives at the other cnd at time $t_{1}$, She swims hack and arrives at the starting position at time $t_{2}$. If she is swimming initially in the positive $x$ direction, determine her average wrioritics symbolically in (a) the lirst hatr of the swim, (b) the second hall' of the swim, and (c) the round trip. (d) What is her average speed for the round trip?

$\mathrm{An}$ athlete leaves one end of a pool of length $L$ at $t=0$
S and arrives at the other cnd at time $t_{1}$, She swims hack and arrives at the starting position at time $t_{2}$. If she is swimming initially in the positive $x$ direction, determine her average wrioritics symbolically in (a) the lirst hatr of the swim,
(b) the second hall' of the swim, and (c) the round trip.
(d) What is her average speed for the round trip?

Key Concepts

Segmented Motion Analysis

Segmented motion analysis involves breaking a motion into distinct parts or intervals and analyzing each segment separately before combining the results. This technique is useful in cases where the motion changes its characteristics, such as a change in direction or speed, and can help in computing average velocities and speeds over different intervals or over the entire journey.

Kinematics of Motion

Kinematics involves the study of motion without considering the forces that cause the motion. In problems related to swimming or any linear motion, kinematics provides tools to calculate quantities such as displacement, distance traveled, time intervals, and average velocity, helping to analyze motion along a straight line or more complex paths.

Average Velocity

Average velocity is defined as the total displacement divided by the total elapsed time. It is a vector quantity that takes into account both the magnitude and the direction of the motion. When computing average velocity, one is interested in how far and in what overall direction the object has moved from its initial to its final position, irrespective of the path taken.

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. Unlike average velocity, average speed is a scalar quantity that only considers the overall distance covered, without any regard for the direction of motion. This concept is particularly useful when the path includes changes in direction.

Displacement

Displacement is the change in position of an object and is calculated as the difference between the final and initial positions, keeping in account the direction. It is a vector quantity and plays a central role in determining average velocity, especially in problems involving return trips or changes in direction.

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