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A football quarterback runs 12.1 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 2.30 s. He breaks the tackle and runs straight forward another 18.3 m in 5.20 s. Calculate his average velocity for each of the three intervals and for the entire motion. (Define the positive direction to be the direction of initial motion.)

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Answer

given,

Case 1: Football straight run 12.1 m for 2.50 s

Case 2: Football moves backward 3 m for 2.30 s

Case 3: Football again move forward 18.3 m for 5.20 s.

Speed on the Three cases,

Case 1

   [tex]v_1 = \dfrac{12.1}{2.50}[/tex]

            v₁ = 4.84 m/s

Case 2

   [tex]v_2 = \dfrac{-3}{2.30}[/tex]

            v₂ = -1.30  m/s

Case 3

   [tex]v_3 = \dfrac{18.3}{5.20}[/tex]

            v₃ = 3.45  m/s

now, Average velocity of the entire motion

  [tex]v_{avg}=\dfrac{total\ distnace}{total\ time}[/tex]

  [tex]v_{avg}=\dfrac{12.1-3+18.3}{2.50+2.30+5.20}[/tex]

  [tex]v_{avg}=\dfrac{27.4}{10}[/tex]

  [tex]v_{avg} = 2.74\ m/s[/tex]

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