ginal cost and margin ment of performance special cases of a sing This is an illustr abstractness. A single ferent interpretations ematical concept once the sciences. This is n each separate science cinctly: "Mathematic analogies that unite th 3.8 Exercises 1-4 A particle moves according to a law of motion s = f(t), t > 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram like Figure 2 to illustrate the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity, and acceleration functions for OSIE 8. (i) When is the particle speeding up? When is it slowing down 1. f (t) = 13 - 1212 + 361 2. f (t) = 0.01+4 - 0.04t 3. f (1) = cos( 171/ 4), 1 = 10 4. f ( t ) = te -1/2