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An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x-direction, determine her average velocities symbolically for the following. (Assume that time t2 is from the other end of the pool to the starting point. Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only. Indicate the direction with the sign of your answer.)

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Answer:

[tex]v_1=\frac{L}{t_1}[/tex]

[tex]v_2=\frac{-L}{t_2}[/tex]

[tex]v_{avg}=\frac{L-L}{t_1+t_2} =0[/tex]

Explanation:

Given:

  • length of the pool along which the athlete swims, [tex]L[/tex]
  • time taken to swim in the positive x-direction from the start of the pool, [tex]t_1[/tex]
  • time taken to return from the end of the pool to the starting point, [tex]t_2[/tex]

Velocity of the athlete from start to the end of the pool in positive direction:

[tex]\rm velocity=\frac{displacement}{time}[/tex]

[tex]v_1=\frac{L}{t_1}[/tex]

Velocity of the athlete from end returning to the start of the pool in negative direction:

Here we have the negative displacement.

[tex]v_2=\frac{-L}{t_2}[/tex]

Now the total average velocity:

[tex]\rm v_{avg}=\frac{total\ displacement}{total\ time}[/tex]

Here we have total displacement as zero because the athlete is finally at the initial starting point.

so,

[tex]v_{avg}=\frac{L-L}{t_1+t_2} =0[/tex]

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