In a time of t seconds, a particle moves a distance of s meters from its starting point, where s = 6t^2 + 4. (a) Find the average velocity between t = 1 and t = 1 + k if (i) h = 0.1 (ii) h = 0.01 (iii) h = 0.001 Enter the exact answers.
(i) When h = 0.1, the average velocity between t = 1 and t = 1 + h is m/sec.
(ii) When h = 0.01, the average velocity between t = 1 and t = 1 + h is m/sec.
(iii) When h = 0.001, the average velocity between t = 1 and t = 1 + h is m/sec.
(b) Use your answers to part (a) to estimate the instantaneous velocity of the particle at time t = 1. Round your estimate to the nearest integer. The instantaneous velocity appears to be m/sec.