Explanation Given information: a-t curve at t=2s, v=0. The a-t curve is first approximated with a series of rectangles; each of width Δ t = 0.25 s . The area of each rectangle is approximately equal to the change in velocity Δ v for the specified interval of time. Thus, Δ v ≃ a a v e Δ t Where the values of a a v e and Δ v are given in columns 1 and 2 respectively, of the table. Now, v ( 2 ) = v 0 + ∫ 0 2 a d t = 0 And approximating the area ∫ 0 2 a d t under the a-t curve by Σ a a v e Δ t ≈ Σ Δ v , the initial velocity is then equal to v 0 = − Σ Δ v Then using, v 2 = v 1 + Δ v 12 Where Δ v 12 is the change in velocity between times t 1 and t 2 , the velocity at the end of each 0 To determine (b) The distance by piston rod as it is brought to rest.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.3, Problem 11.81P

To determine

(a)

The initial velocity of the piston rod.

To determine

(b)

The distance by piston rod as it is brought to rest.

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Chapter 11.3, Problem 11.80P

Chapter 11.3, Problem 11.82P

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(a) The initial velocity of the piston rod.

Solution Summary: The author illustrates the a-t curve at t=2s, v=0. The area of each rectangle is approximately equal to the change in velocity for the specified interval of time.