Answer
$K = 2600~J$
Work Step by Step
We can find the acceleration:
$x = \frac{1}{2}at^2$
$a = \frac{2x}{t^2}$
$a = \frac{(2)(7.0~m)}{(1.6~s)^2}$
$a = 5.47~m/s^2$
We can find the speed at the end of the $1.6~s$:
$v_f = v_0+at$
$v_f = 0+at$
$v_f = (5.47~m/s^2)(1.6~s)$
$v_f = 8.75~m/s$
The speed at the end of the $~~1.6~s~~$ is $~~8.75~m/s$
We can find the sprinter's mass:
$m = \frac{670~N}{9.8~m/s^2} = 68.37~kg$
We can find the kinetic energy:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}(68.37~kg)(8.75~m/s)^2$
$K = 2600~J$
