Consider a relativistic particle of mass m and kinetic energy T. Derive an expression for the particle's speed u in terms of T and m. Make a table showing both the correct value of u and the value that you would get if you assumed that T=mu2/2, for T = 0.001mc2, 0.01mc2, 0.1mc2, andmc2. Find the percent discrepancy for each case. Approximately find what is the largest value of T for which a non-relativistic calculation of u is within 1 percent of the correct value?