(a) Explanation Given information: The acceleration of the particle is a = − k x . The initial velocity ( v 0 ) is 15 ft/s. The initial velocity ( v f ) is 9 ft/s. The initial position ( x 0 ) is 0.6 ft. The final position ( x f ) is 1.2 ft. Calculation: Write the acceleration of the particle in terms of rate of change of velocity: a = v d v d x Here, acceleration of particle is a , change in velocity is dv , and change in position is dx . Rewrite the above equation: v d v = a d x Integrate the above equation and apply the limits. ∫ v 0 v f v d v = a ∫ x 0 x f d x (1) When v 0 = 15 ft/s and x 0 = 0.6 ft : Substitute − k x for a in Equation (1) and apply the integration. ∫ 15 v f v d v = − k ∫ 0.6 x f d x x 1 2 v f 2 − 1 2 ( 15 ) 2 = − k ln x | 0.6 x f 1 2 v f 2 − 1 2 ( 15 ) 2 = − k ln ( x f 0 (b) To determine The position of the particle when velocity is zero.

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 11.1, Problem 11.17P

(a)

To determine

The velocity of the particle when the position is 1.5 ft.

(b)

To determine

The position of the particle when velocity is zero.

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Chapter 11.1, Problem 11.16P

Chapter 11.1, Problem 11.18P

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