(a) Explanation Given information: The constant acceleration ( a 1 ) of particle at 6 sec is − 4 ft/s 2 . The acceleration is zero from 6sec to 10 sec. From 10 sec to 14 sec the acceleration ( a 2 ) of the particle is 4 ft/s 2 . The velocity ( v 0 ) of the particle at origin is 16 ft/s . Calculation: Show a - t curve of particle that moves in a straight line as in Figure (1). Calculate the area ( A 1 ) using the relation: A 1 = t 1 a 1 Substitute 6 sec for t 1 and − 4 ft/s 2 for a 1 A 1 = ( 6 ) × ( − 4 ) = − 24 ft/s Calculate the area ( A 2 ) using the relation: A 2 = t 3 a 2 Substitute 4 sec for t 3 and 4 ft/s 2 for a 1 A 2 = ( 4 ) × ( 4 ) = 16 ft/s Calculate the velocity ( v 6 ) at the origin using the relation: v 6 = v 0 + A 1 Substitute 16 ft/s for v 0 and − 24 ft/s for A 1 . v 6 = 16 + ( − 24 ) = − 8 ft/s Calculate the velocity ( v 10 ) at 10 sec using the relation; v 10 = v 6 Substitute − 8 ft/s for v 6 . v 10 = − 8 ft/s Calculate the velocity ( v 14 ) at 14 sec using the relation: v 14 = v 10 + A 2 Substitute − 8 ft/s for v 10 and 16 ft/s for A 2 . v 14 = − 8 + 16 = 8 ft/s Tabulate the acceleration ( a ), velocity ( v ) corresponding to time ( t ) as in Table (1): t ( s ) a ( ft / s 2 ) v ( ft / s ) 0 -4 16 6 0 -8 10 0 -8 14 4 8 Show v - t curve of particle that moves in a straight line with areas as in Figure (2). Calculate the area ( A 3 ) using the relation: A 3 = 1 2 v 0 t 4 Here, t 4 is 0 sec to 4 sec. Substitute 4 sec for t 4 and 16 ft/s for v 0 . A 3 = 1 2 ( 16 ) ( 4 ) = 32 ft Calculate the area ( A 4 ) using the relation: A 4 = 1 2 v 6 t 5 Here, t 5 is 4 sec to 6 sec. Substitute 2 sec for t 5 and − 8 ft/s for v 6 . A 4 = 1 2 ( − 8 ) ( 2 ) = − 8 ft Calculate the area ( A 5 ) using the relation: A 5 = t 6 v 10 Here, t 6 is 6 sec to 10 sec Substitute 4 sec for t 6 and − 8 ft/s for v 10 (b) To determine The amount of time ( Δ t ) during which the particle is further than 16 ft from the origin.

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 11.3, Problem 11.62P

(a)

To determine

Construct the v−t and x−t curves for 0≤t≤14sec.

(b)

To determine

The amount of time (Δt) during which the particle is further than 16 ft from the origin.

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Chapter 11.3, Problem 11.61P

Chapter 11.3, Problem 11.63P

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Construct the v − t and x − t curves for 0 ≤ t ≤ 14 sec .

Solution Summary: The author calculates the v-t and x-T curves of particle that moves in a straight line as in Figure (1).