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A single, non-constant force acts in the x direction on an object of mass m that is constrained to move along the x-axis. As a result the object\'s position as a function of time is:x(t)=P+Qt+Rt^3How much work is done by this force from t = 0 s to final time T? Express your answer in terms of P, Q, R, m, and T.

Respuesta :

Answer:

Work done is given as

[tex]W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)[/tex]

Explanation:

As we know that the position of object is given as

[tex]x(t) = P + Qt + Rt^3[/tex]

now we know that rate of change in position of object is known as velocity

so we have

[tex]v = \frac{dx}{dt}[/tex]

[tex]v = Q + 3Rt^2[/tex]

now we have

initial speed at t = 0

[tex]v_i = Q[/tex]

at t = T final speed is given as

[tex]v_f = Q + 3RT^2[/tex]

now work done is change in kinetic energy

[tex]W = \frac{1}{2}m(v_f^2 - v_i^2)[/tex]

[tex]W = \frac{1}{2}m[(Q + 3RT^2)^2 - Q^2][/tex]

[tex]W = \frac{1}{2}m(2Q + 3RT^2)(3RT^2)[/tex]

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