A rocket sled having an initial speed of 150 mi/hr is slowed by a channel of water. Assume that during the braking process, the acceleration a is given by a(v)=-mu v , where v is the velocity and mu is a constant. If it requires a distance of 2000 ft to slow the sled to 15 mi/hr, determine the value of mu?

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I was able to understand the attached problem and have the answer now for mu.  So the equation I have is 

v=150e-6.0788 x

My question, then, is how do we find the TIME to slow the sled to 15 mi/hr ? The answer is supposed to be 35.533 seconds, but I don't know how to get that.  Thanks!

### Problem Statement:

A rocket sled having an initial speed of 150 mi/hr is slowed by a channel of water. Assume that during the braking process, the acceleration \( a \) is given by \( a(v) = -\mu v^2 \), where \( v \) is the velocity and \( \mu \) is a constant.

If it requires a distance of 2000 ft to slow the sled to 15 mi/hr, determine the value of \( \mu \).

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In this problem, we are tasked with finding the constant \( \mu \) that defines the deceleration of a rocket sled slowed by water resistance. The initial and final speeds, as well as the distance required for the sled to slow down, are given. The relationship between acceleration and velocity should be integrated to solve for \( \mu \).

No graphs or diagrams are provided in this problem statement. The focus is on applying physics and calculus concepts to an equation involving deceleration due to water resistance.

To proceed, you would likely use principles from calculus to integrate the given equation for acceleration and solve for the constant \( \mu \).
Transcribed Image Text:### Problem Statement: A rocket sled having an initial speed of 150 mi/hr is slowed by a channel of water. Assume that during the braking process, the acceleration \( a \) is given by \( a(v) = -\mu v^2 \), where \( v \) is the velocity and \( \mu \) is a constant. If it requires a distance of 2000 ft to slow the sled to 15 mi/hr, determine the value of \( \mu \). --- In this problem, we are tasked with finding the constant \( \mu \) that defines the deceleration of a rocket sled slowed by water resistance. The initial and final speeds, as well as the distance required for the sled to slow down, are given. The relationship between acceleration and velocity should be integrated to solve for \( \mu \). No graphs or diagrams are provided in this problem statement. The focus is on applying physics and calculus concepts to an equation involving deceleration due to water resistance. To proceed, you would likely use principles from calculus to integrate the given equation for acceleration and solve for the constant \( \mu \).
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