(a) Explanation Given information: The acceleration ( a ) of particle is k ( 1 − e − x ) . The velocity ( v ) of the particle is 9 m/s . The position ( x ) of the particle is − 3 m . Calculation: Write the relation for the acceleration ( a ) as given below: a = k ( 1 − e − x ) Here, k is constant. Express acceleration ( a ) by differentiation velocity ( v ) with respective to distance ( x ): a = v d v d x Substitute k ( 1 − e − x ) for a . k ( 1 − e − x ) = v d v d x v d v = k ( 1 − e − x ) d x Apply integration. ∫ 9 v v d v = ∫ − 3 x k ( 1 − e − x ) d x Integrate the above equation. [ 1 2 v 2 ] 9 v = [ k ( x + e − x ) ] − 3 x 1 2 v 2 − 1 2 9 2 = k ( x + e − x ) − k ( ( − 3 ) + e − ( − 3 ) ) 1 2 v 2 − 40 (b) To determine The velocity ( v ) of the particle when position ( x ) is 2 m .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Chapter 11.1, Problem 11.21P

(a)

To determine

The value of constant (k).

(b)

To determine

The velocity (v) of the particle when position (x) is 2 m.

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Chapter 11.1, Problem 11.20P

Chapter 11.1, Problem 11.22P

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The value of constant ( k ).

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