contestada

If a force does a positive amount of work on an object, does the object's speed
increase, decrease, or remain the same? Justify your answer.

Respuesta :

The speed of the object increases

Explanation:

We can answer this question by applying the work-energy theorem, which states that the work done on an object is equal to the change in kinetic energy of the object. Mathematically:

[tex]W=K_f -K_i= \frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]

where

W is the work done on the object

[tex]K_f, K_i[/tex] are the final and initial kinetic energy of the object, respectively

m is the mass of the object

v is its final speed

u is its initial speed

In this case, the force does a positive amount of work on the object, so

[tex]W>0[/tex]

This also implies that

[tex]K_f > K_i[/tex]

And so

[tex]\frac{1}{2}mv^2 > \frac{1}{2}mu^2[/tex]

And therefore

[tex]v>u[/tex]

which means that the speed of the object increases.

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