Final answer:
The question asks to find the surface area of a solid of revolution for a specific curve. The actual calculation requires using the formula for the surface area of a solid of revolution and integrating it with respect to arc length, not the unrelated physics equations provided.
Step-by-step explanation:
The student has asked to find the exact area of the surface obtained by rotating the curve defined by x=t³ and y=t² for 0≤t≤1 about the x-axis. To solve this, we would normally use the formula for the surface area of a solid of revolution, which for a curve rotated about the x-axis is given by S = 2π ∫ y ∙ ds, where ds is an element of arc length on the curve.
The arc length element ds can be calculated from the derivatives of x and y with respect to t using ds = √(dx/dt)² + (dy/dt)² dt. However, the provided information seems to be a mix-up of formulas and concepts from different physics contexts, including special relativity and rotational kinematics, which are not directly applicable to this calculus problem.