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Consider two tanks where initially each tank contains 100 gallons of fresh water. A salt...

Question:

A section of a bike trail can be described by y=0.0016x² . On this section of the trail a bike maintains a constant vx=650 m/min. What is the bike's velocity when x=100m?

Velocity

The velocity is given by the rate of change of position with respect to time. It is a vector quantity and hence needs to be represented as a vector. Therefore in this question, the x and y components can be calculated separately and represented as a vector.

Answer and Explanation:

Since the shape of the path is given by {eq}y=0.0016x^2 {/eq}, differentiating both sides,

{eq}\frac{dy}{dt} = 0.0032x\frac{dx}{dt}=0.0032 \cdot 100 \cdot 650 m/min = 208 m/min {/eq}

Therefor, the total velocity is {eq}650\hat{\mathbf{x}}+208\hat{\mathbf{y}} {/eq}.


Learn more about this topic:

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Derivatives: The Formal Definition

from Math 104: Calculus

Chapter 7 / Lesson 5
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