Module 14  Related Rates 
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  SelfTest 
Lesson 14.4: A Moving Particle 
A final relatedrate problem, which models a particle moving along a curve, is explored in this lesson. A particle is moving along the curve y = x^{3}. At a certain instant, the particle is at the point (2, 8) and dx/dt = 5 ft/sec. How fast is the distance s from the particle to the origin changing at that instant? Find the Distance Function s(t)
Find dy/dt at the Point (2, 8) We know that dx/dt = 5 at this point. Thus, we need to compute dy/dt with the restrictions that x(t)=2, y(t)=8, and d(x(t),t)=5. So, dy/dt = 60 ft/sec at the point (2, 8). Answering the Question To find out how fast the distance s from the particle to the origin is changing at the specified instant, we need to compute ds/dt with the restrictions that x(t)=2, y(t)=8, dx/dt=5, and dy/dt=60. Therefore, the particle is moving away from the origin at 
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