Final answer:
The correct relation between a body's momentum (p) and its kinetic energy (K) when moving at a constant speed (v) is p = √(2mK), which is option A. Other options are incorrect due to faulty relationships between momentum, kinetic energy, and velocity.
Step-by-step explanation:
The relationship between a body's mass (m), speed (v), kinetic energy (K), and momentum (p) can be understood by recalling the definitions of kinetic energy and momentum. The kinetic energy (K) is given by the expression K = (1/2)mv2 and the momentum (p) is the product of mass and velocity, given by p = mv.
To find the correct relationship between kinetic energy and momentum for a body moving at a constant speed, we can manipulate these equations. From the kinetic energy definition, we can express momentum in terms of kinetic energy as p = √(2mK). To prove that, we substitute K = (1/2)mv2 into the momentum definition where p = mv, then solve for p:
p = mv = √(m2v2) = √(2m(½mv2)) = √(2mK).
Therefore, the correct relationship between momentum and kinetic energy in this context is p = √(2mK), which corresponds to option A. The other options are incorrect upon examination. For instance, option B is simply a typo error that has m and k in the wrong order. Option C implies 2K = pv, but plugging the values of p and v as stated does not hold true as 2(½mv2) ≠ mv2. Lastly, option D is incorrect because it appears to be solving for v in terms of p and k without the correct manipulations.