# College Physics Problem 2.14

#### A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.

SOLUTION:

a) The average velocity for each interval is computed using the formula

$v=\frac{x}{t}$

For the first interval

$v_1=\frac{15.0\:m}{2.50\:s}=6.00\:m/s$

For the second interval

$v_2=\frac{-3.00\:m}{1.75\:s}=-1.71\:m/s$

For the third interval

$v_3=\frac{21.0\:m}{5.20\:s}=4.04\:m/s$

b) For the entire motion, we need displacement from the beggining to the end.

$v=\frac{displacement}{time}$

$v=\frac{15\:m-3\:m+21\:m}{2.50\:s\:+1.75\:s\:+5.20\:s}$

$v=\frac{33\:m}{9.45\:s}$

$v=3.49\:m/s$

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