A runner whose mass is $53$ kg accelerates from a stop to a speed of $6$ m$/$s in $3$ seconds. $($A good sprinter can run $100$ meters in about $10$ seconds, with an average speed of $10$ m$/$s$.)$

$($a$)$ What is the average horizontal component of the force that the ground exerts on the runner's shoes?

Average force $=$ N

$($b$)$ How much displacement is there of the force that acts on the sole of the runner's shoes, assuming that there is no slipping?

Displacement $=$ m

$($c$)$ Therefore, how much work is done on the extended system $($the runner$)$ by the force you calculated in part $($b$)?$

Work $=$ J

$($d$)$ How much work is done on the point$-$particle system by this force? $($Hint: use a fundamental principle, as applied to the point$-$particle system.$)$

Work $=$ J

$($e$)$ The kinetic energy of the runner increases; what kind of energy decreases? $($In this short run, there has not been a significant temperature change in the runner.$)$

chemical energygravitational energy$$translational kinetic energythermal energyrotational kinetic energy

$($f$)$ What is the change of the energy you identified in part $($e$)?$ Pay attention to signs.

Energy change $=$ J