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A 56 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

Respuesta :

skyluke89
The sprinter is in uniform accelerated motion, and its initial velocity is zero, so the relationship betwen space (S) and time (t) is
[tex]S= \frac{1}{2} a t^2[/tex]
where a is the acceleration. Using the data of the problem, we can find a:
[tex]a= \frac{2S}{t^2} = \frac{2 \cdot 49 m}{(7.0 s)^2} =2.0 m/s^2[/tex]
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
[tex]v(t)=at=(2.0 m/s^2)(2.0 s)=4.0 m/s[/tex]

the kinetic energy of the sprinter is
[tex]K= \frac{1}{2} mv^2= \frac{1}{2}(56 kg)(4.0 m/s)^2=448 J [/tex]

and so the power output is
[tex]P= \frac{E}{t} = \frac{448 J}{2.0 s} =224 W[/tex]

b) power output at t=4.0s 
The velocity at t=4.0 s is
[tex]v(t)=at=(2.0 m/s^2)(4.0 s)=8.0 m/s[/tex]

the kinetic energy of the sprinter is
[tex]K= \frac{1}{2} mv^2= \frac{1}{2}(56 kg)(8.0 m/s)^2=1792 J [/tex]

and so the power output is
[tex]P= \frac{E}{t} = \frac{1792 J}{4.0 s} =448 W[/tex]

c) Power output at t=6.0 s
The velocity at t=2.0 s is
[tex]v(t)=at=(2.0 m/s^2)(6.0 s)=12.0 m/s[/tex]

the kinetic energy of the sprinter is
[tex]K= \frac{1}{2} mv^2= \frac{1}{2}(56 kg)(6.0 m/s)^2=4032 J [/tex]

and so the power output is
[tex]P= \frac{E}{t} = \frac{4032 J}{6.0 s} =672 W[/tex]
onyebuchinnaji

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 kg
  • initial velocity of the sprinter, u = 0
  • distance covered by the sprinter, s = 49 m
  • time 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;

[tex]Power \ 0utput= \frac{Energy}{time} = \frac{F \times d}{t} \\\\Power \ 0utput= \frac{112 \times 49}{2} = 2,744 \ J/s[/tex]

The sprinter's power output at 4.0 s;

[tex]Power \ 0utput= \frac{Energy}{time} = \frac{F \times d}{t} \\\\Power \ 0utput= \frac{112 \times 49}{4} = 1,372 \ J/s[/tex]

The sprinter's power output at 6.0 s;

[tex]Power \ 0utput= \frac{Energy}{time} = \frac{F \times d}{t} \\\\Power \ 0utput= \frac{112 \times 49}{6} = 914.67 \ J/s[/tex]

Learn more here:https://brainly.com/question/19415290

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