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Starting at t = 0 a net external force in the +x-direction is applied to an object that has mass 5.00 kg. A graph of the force as a function of time is a straight line that passes through the origin and has slope 5.00 N/s.
If the object is at rest at t = 0 what is the magnitude of the force when the object has reached a speed of 9.00 m/s?
Express your answer with the appropriate units.

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sqdancefan

Answer:

  15√2 N

Explanation:

The acceleration is given by ...

  a = F/m = 5t/5 = t . . . . meters/second^2

The velocity is the integral of acceleration:

  v = ∫a·dt = (1/2)t^2

This will be 9 m/s when ...

  9 = (1/2)t^2

  t = √18 . . . . seconds

And the force at that time is ...

  F = 5(√18) = 15√2 . . . . newtons

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