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 .

Velocity  

               V  = Q + 3Rt²

at t = 0, = Q + 3r(0) ==> Q

at t = T, = Q + 3rT²

Work done (W) = ΔKE =

W =

W =   [Q² + 9R²T⁴ + 2Q(3RT²) - Q²]

W =   (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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