A particle moves along the curve . As the particle passes through the point , its co-ordinate increases at a rate of . How fast is the distance from the particle to the origin changing at this instant?
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Moving Point A particle is moving along the graph of
(see figure). When , the y-component of the position of the particle is increasing at the rate of 1 centimeter per second.
(a) How fast is the x-component changing at this moment?
(b) How fast is the distance from the origin changing at this moment?
(c) How fast is the angle of inclination changing at this moment?
A particle moves along the path y=5x3 with unit speed. How fast is the tangent turning when the particle passes through the point (1,5)?
(Hint use the Kappa(s)=|d/ds| )
EXPLORING CONCEPTS
Think About It Consider a particle that is moving along the space curve given by . Write a vector-valued function for a particle that moves four times as fast as the particle represented by . Explain how you found the function.
