2.7 EXERCISES 1-4 A particle moves according to a law of motion s f(t), t 0, where t is measured in seconds ands in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (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 6 seconds. (f) Draw a diagram like Figure 2 to illustrate the motion of the particle. (g) Find the acceleration at time t and after 1 second. (h) Graph the position, velocity, and acceleration functions for 0t 6. (i) When is the particle speeding up? When is it slowing down? 1. f(t) t3-9t224t 2. f(t) 0.01t - 0.04t3

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.