iamthepantaloon3885 iamthepantaloon3885
  • 06-08-2017
  • Physics
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Find expressions for the force needed to bring an object of mass m from rest to speed v in time t. express your answer in terms of the variables m, v, and t.

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Ferraz
Ferraz Ferraz
  • 06-08-2017
Good morning.

We have that:

[tex]\mathsf{V = a\cdot t}[/tex] , since we have rest in the inicial time.

The acceleration can be found with Newton's Law:

[tex]\mathsf{F = m\cdot a\iff a = \dfrac{F}{m}} [/tex]

Now we put the acceleratin in the velocity equation:

[tex]\mathsf{V = \dfrac{F}{m} \cdot t}[/tex]

We want the force, so, let's isolate F:

[tex]\mathsf{V\cdot m = F\cdot t}\\ \\ \\ \boxed{\mathsf{F = \dfrac{V\cdot m}{t}}}[/tex]

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