A56 kg sprinter, starting from rest, runs 49 m in 7.0 s at constant acceleration. what is the sprinter's power output at 2.0 s, 4.0 s, and 6.0 s

The sprinter's power output at 2.0  is 2,744 J/s.

The sprinter's power output at 4.0 s is 1,372 J/s.

The sprinter's power output at 6.0 s is 914.67 J/s.

The given parameters;

mass of the sprinter, m = 56 kginitial velocity of the sprinter, u = 0distance covered by the sprinter, s = 49 mtime of motion of the sprinter, t = 7.0 s

The acceleration of the sprinter is calculated as follows;

s = u + ¹/₂at²

49 = 0 + (7² x 0.5)a

49 = 24.5a

a = 2 m/s²

The force exerted by the sprinter is calculated as follows;

F = ma

F = 56 x 2

F = 112 N

The sprinter's power output at 2.0 s;

The sprinter's power output at 4.0 s;

The sprinter's power output at 6.0 s;

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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

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