The sprinter is in uniform accelerated motion, and its initial velocity is zero, so the relationship betwen space (S) and time (t) is
where a is the acceleration. Using the data of the problem, we can find a:
So now we can solve the 3 parts of the problem.
a) power output at t=2.0 s
The velocity at t=2.0 s is
the kinetic energy of the sprinter is
and so the power output is
b) power output at t=4.0s
The velocity at t=4.0 s is
the kinetic energy of the sprinter is
and so the power output is
c) Power output at t=6.0 s
The velocity at t=2.0 s is
the kinetic energy of the sprinter is
and so the power output is
where a is the acceleration. Using the data of the problem, we can find a:
So now we can solve the 3 parts of the problem.
a) power output at t=2.0 s
The velocity at t=2.0 s is
the kinetic energy of the sprinter is
and so the power output is
b) power output at t=4.0s
The velocity at t=4.0 s is
the kinetic energy of the sprinter is
and so the power output is
c) Power output at t=6.0 s
The velocity at t=2.0 s is
the kinetic energy of the sprinter is
and so the power output is