A single, nonconstant force acts in the + x ‑direction on an object of mass M that is constrained to move along the x ‑axis. As

Question

A single, nonconstant 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 + Q t + R t 3 How much work W is done by this force from t = 0 s to final time T ? Express the answer in terms of P , Q , R , M , and T .

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Orla Orla 3 months 2021-08-15T07:37:59+00:00 1 Answers 1 views 0

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    2021-08-15T07:39:16+00:00

    Answer:

    Velocity  V = \frac{dx}{dt} = \frac{d}{dt} (P + Qt + Rt^{3})

                   V = 0 + Q(1) + 3Rt^{2}

                   V  = Q + 3Rt²

    at t = 0, v_{i} = Q + 3r(0) ==> Q

    at t = T, v_{f} = Q + 3rT²

    Work done (W) = ΔKE = \frac{1}{2} m(v_f^{2} - v_i^{2})

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

    W =  \frac{1}{2} m [Q² + 9R²T⁴ + 2Q(3RT²) – Q²]

    W =  \frac{1}{2} m (9R²T⁴ + 6QRT²)

    Explanation:

    Differentiate the position.

    Find the equation for speed.

    Find the initial and final speed.

    Use work energy theorem to find the work done by finding the change in kinetic energy.

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