(a) Explanation Given Information: The initial velocity ( v 0 ) of the particle is − 2 m/s . Calculation: Show the a-t curve of the given particle with area as in Figure (1). Calculate the area ( A 1 ) using the relation: A 1 = a 1 t 1 Here, a 1 is acceleration from 0 sec to 8 sec and t 1 is time between 0 sec to 8sec. Substitute − 0.75 m/s 2 for a 1 and 8 sec for t 1 . A 1 = − 0.75 × 8 = − 6 m/s Calculate the area ( A 2 ) : A 2 = a 2 t 2 Here, a 2 is acceleration from 8 sec to 12 sec and t 2 is time between 8 sec to 12 sec. Substitute 2 m/s 2 for a 2 and 4 sec for t 2 . A 2 = 2 × 4 = 8 m/s Calculate the area ( A 3 ) : A 3 = a 3 t 2 Here, a 3 is acceleration from 12 sec to 18 sec and t 3 is time between 12 sec to 18 sec. Substitute 6 m/s 2 for a 3 and 6 sec for t 3 . A 3 = 6 × 6 = 36 m/s Calculate the velocity ( v 8 ) at time 8 sec using the relation: v 8 = v 0 + A 1 Substitute − 6 m/s for A 1 and − 2 m/s for v 0 . v 8 = − 2 + ( − 6 ) = − 8 m/s Calculate the velocity ( v 12 ) at time 12 sec using the relation: v 12 = v 8 + A 2 Substitute 8 m/s for A 2 and − 8 m/s for v 8 . v 12 = − 8 + 8 = 0 m/s Calculate the velocity ( v 18 ) at time 18 sec using the relation: v 18 = v 12 + A 3 Substitute 36 m/s for A 3 and 0 m/s for v 12 . v 18 = 0 + 36 = 36 m/s Tabulate the velocity (v) corresponding to time (t) as in Table (1). Time ( t )(s) Velocity ( v ) ( m/s ) 0 -2 8 -8 12 -0 18 36 Plot the v-t curve for the particle as in Figure (2) (b) To determine The positon ( x 18 ) , velocity ( v 18 ) and total distance ( d ) traveled when time is 18 sec.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 11.3, Problem 11.88P

(a)

To determine

Construct the v-t and x-t curve for 0<t<18sec.

(b)

To determine

The positon (x18) , velocity (v18) and total distance (d) traveled when time is 18 sec.

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Chapter 11.3, Problem 11.87P

Chapter 11.4, Problem 11.3CQ

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Construct the v-t and x-t curve for 0 < t < 18 sec .

Solution Summary: The author shows the a-t curve of the given particle with area as in Figure (1).

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Construct the v-t and x-t curve for 0<t<18sec.

The positon (x18) , velocity (v18) and total distance (d) traveled when time is 18 sec.

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Chapter 11 Solutions

Construct the v-t and x-t curve for 0 &lt; t &lt; 18 sec .

Solution Summary: The author shows the a-t curve of the given particle with area as in Figure (1).

Concept explainers

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Construct the v-t and x-t curve for 0<t<18sec.

The positon (x18) , velocity (v18) and total distance (d) traveled when time is 18 sec.

Want to see the full answer?

Chapter 11 Solutions

Construct the v-t and x-t curve for 0 < t < 18 sec .