# Sec 3.7: Rates of Change in the Natural and Social Sciences

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Sec 3.7: Rates of Change in the Natural and Social Sciences
Syllabus: Example 1 only instantaneous rate of change of S with respect to t S = distance in meter t = time in seconds instantaneous velocity instantaneous acceleration

Sec 3.7: Rates of Change in the Natural and Social Sciences
(a) Find the velocity at time t (b) What is the velocity after 2 s? After 4 s ? (c) When the particle at rest?

Sec 3.7: Rates of Change in the Natural and Social Sciences
(d) When is the particle moving forward ( that is , in the positive direction ) (e) Draw a diagram to represent the motion of the particle

Sec 3.7: Rates of Change in the Natural and Social Sciences
(f) Find the total distance traveled by the particle during the first five seconds (g) Find the acceleration at time t and after 4 s.

Sec 3.7: Rates of Change in the Natural and Social Sciences
(h) Graph the position, velocity, and acceleration functions for 0<t<5

Sec 3.7: Rates of Change in the Natural and Social Sciences
(i) When is the particle speeding up? When is it slowing down? speed up? v & a have same sign slow down? v & a have opposite sign

Sec 3.7: Rates of Change in the Natural and Social Sciences

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