Straight-line graphs of kinetic energy K versus the square of speed v² are obtained for two bodies X and Y moving on a frictionless surface. Both lines pass through the origin. The slope of the line for X is 2.8 J·s² m⁻², whereas that for Y is 4.0 J·s² m⁻².
Answer the following questions.
a. (i) Derive an expression relating the slope of a K–v² graph to the mass of the body.
b. (ii) Calculate the masses of bodies X and Y.
c. (iii) Find the kinetic energy of each body when its speed is 6 m/s.
d. (iv) At what speed will the kinetic energies of X and Y differ by 30 J?