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5/ Determine the rate, wit to time, at which the C acceleration is changing Pnstant that s- 10Em/s increasing at a rate OF 30 and the 00 an radius is 50 Of 2 cm/s. at a rate

5/ Determine the rate, wit to time, at which the C acceleration is changing Pnstant that s- 10Em/s increasing at a rate OF 30 and the 00 an radius is 50 Of 2 cm/s. at a rate

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** Determine the rate, with respect to time, at which the centripetal acceleration is changing at the instant that \( s = 10 \, \text{cm/s} \) and is increasing at a rate of \( 3 \, \text{cm/s}^2 \), and the radius is \( 50 \, \text{cm} \) and is decreasing at a rate of \( 2 \, \text{cm/s} \).
Transcribed Image Text:**Problem Statement:** Determine the rate, with respect to time, at which the centripetal acceleration is changing at the instant that \( s = 10 \, \text{cm/s} \) and is increasing at a rate of \( 3 \, \text{cm/s}^2 \), and the radius is \( 50 \, \text{cm} \) and is decreasing at a rate of \( 2 \, \text{cm/s} \).
**Centripetal Acceleration of a Particle in Circular Motion** Given a particle moving in a circle, its centripetal acceleration \(q\) in cm/s\(^2\) is given by: \[ q = f(s, r) = \frac{s^2}{r} \] Where: - \(r\) is the radius in cm. - \(s\) is the speed of the particle in cm/s. The quantities \(q\), \(s\), and \(r\) are all functions of time \(t\). --- a) **Exercise: Write out the chain rule for \(\frac{dq}{dt}\).**
Transcribed Image Text:**Centripetal Acceleration of a Particle in Circular Motion** Given a particle moving in a circle, its centripetal acceleration \(q\) in cm/s\(^2\) is given by: \[ q = f(s, r) = \frac{s^2}{r} \] Where: - \(r\) is the radius in cm. - \(s\) is the speed of the particle in cm/s. The quantities \(q\), \(s\), and \(r\) are all functions of time \(t\). --- a) **Exercise: Write out the chain rule for \(\frac{dq}{dt}\).**
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