Chap3_Sec7_Physics

Chap3_Sec7_Physics - PHYSICS Let s = f(t) be the position...

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Let s = f ( t ) be the position function of a particle moving in a straight line. Then, s s / t represents the average velocity over a time period t s v = ds / dt represents the instantaneous velocity (velocity is the rate of change of displacement with respect to time) s The instantaneous rate of change of velocity with respect to time is acceleration: a ( t ) = v’ ( t ) = s’’ ( t ) PHYSICS
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These were discussed in Sections 2.7 and 2.8 s However, now that we know the differentiation formulas, we are able to solve problems involving the motion of objects more easily. PHYSICS
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The position of a particle is given by the equation s = f ( t ) = t 3 – 6 t 2 + 9 t where t is measured in seconds and s in meters. a) Find the velocity at time t . b) What is the velocity after 2 s? After 4 s? c) When is the particle at rest? PHYSICS Example 1
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d) When is the particle moving forward (that is, in the positive direction)? e) Draw a diagram to represent the motion of the particle. f) Find the total distance traveled by the particle during the first five seconds. PHYSICS Example 1
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g) Find the acceleration at time t and after 4 s. h) Graph the position, velocity, and acceleration functions for 0 t 5. i) When is the particle speeding up? When is it slowing down? PHYSICS Example 1
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of the position function. s
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Chap3_Sec7_Physics - PHYSICS Let s = f(t) be the position...

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