Particle Question (calculus required)

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Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: Particle Question (calculus required)
By Justice (Justice) on Tuesday, October 14, 2003 - 03:35 pm: Edit

A particle is moving along the curve y = x^2 - 1, always moving to the right.
Suppose that instead of giving you dy/dt, rather we know that the particle's distance from the origin is changing at the constant rate of 4 in/min. What then must dx/dt be as the particle passes through the point (2,3)?

By Fofisty (Fofisty) on Tuesday, October 14, 2003 - 05:14 pm: Edit

uhh i guess i don't follow... wouldn't dx/dt have to equal 4 (first derivative is velocity)? y=x^2-1 - > y'=2x ... y'(2)=4

By Justice (Justice) on Tuesday, October 14, 2003 - 07:55 pm: Edit

No, for it to be 4, it would be traveling away from the x-axis at 4in/min. Instead, it is traveling in a line that is not perpendicular to the axis but rather has an endpoint on the origin.

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