According to the special theory of relativity, the apparent mass of an object depends on its velocity according to the formula Mg m= (1_ v2)1/2 2 where v is its (sub-light) velocity, m, is the "rest mass" of the object (that is, its mass when v = 0), and c is the velocity of light: approximately 3 x 108 meters per second. (@) If p = mvis the momentum, find d_p v dp _ dv (b) Use the following integral formula for W together with the result in part (a) to find the work required to accelerate an object from a velocity of v, to v;. Vi W=/ vdv Jvg dv W= Thus, the work to accelerate an object from one velocity to another is given by the change from its initial to its final total relativistic energy. (c) Deduce (as Albert Einstein did) that the total relativistic energy E of a body at rest with rest mass m is given by the following famous equation. E=