Explanation Given: The Equation of the position of the particle at is s = [ 2 sin ( π 5 t ) + 4 ] m . Write the given equation of velocity ( v ) of the particle. s = [ 2 sin ( π 5 t ) + 4 ] m (I) Here, t is the time in seconds. Write the formula for velocity ( v ) of the particle. v = d s d t (II) Here, d s d t is rate of change of displacement with respect to time. Write the formula for acceleration ( a ) of the particle. a = d v d t (III) Here, d v d t is rate of change of velocity with respect to time. Conclusion: Calculate the position of the particle at the time interval of 0 s ≤ t ≤ 10 s . When, t = 0 s . Substitute 0 s for t in Equation (I). s = [ 2 sin ( π 5 ( 0 ) ) + 4 ] = 0 + 4 = 4 m When, t = 2.5 s . Substitute 1 s for t in Equation (I). s = [ 2 sin ( π 5 ( 2.5 ) ) + 4 ] = 2 + 4 = 6 m When, t = 5 s . Substitute 5 s for t in Equation (I). s = [ 2 sin ( π 5 ( 5 ) ) + 4 ] = 0 + 4 = 4 m When, t = 7.5 s . Substitute 7.5 s for t in Equation (I). s = [ 2 sin ( π 5 ( 7.5 ) ) + 4 ] = − 2 + 4 = 2 m When, t = 10 s . Substitute 10 s for t in Equation (I). s = [ 2 sin ( π 5 ( 10 ) ) + 4 ] = 0 + 4 = 4 m Plot the s − t graph for the interval of 0 s ≤ t ≤ 10 s as shown in Figure (1). Thus, the s − t graph was plotted and shown in Figure (1). Calculate the velocity ( v ) of the particle at the time interval of 0 s ≤ t ≤ 10 s . Substitute [ 2 sin ( π 5 t ) + 4 ] for s in Equation (II). v = d d t [ 2 sin ( π 5 t ) + 4 ] = 2 ( π 5 cos ( π 5 t ) ) = 2 π 5 cos ( π 5 t ) When, t = 0 s . Substitute 0 s for t in Equation v = 2 π 5 cos ( π 5 t ) . v = 2 π 5 cos ( π 5 ( 0 ) ) = 2 π 5 ( 1 ) = 2 π 5 m/s When, t = 2.5 s . Substitute 2.5 s for t in Equation v = 2 π 5 cos ( π 5 t ) . v = 2 π 5 cos ( π 5 ( 2.5 ) ) = 2 π 5 ( 0 ) = 0 m/s When, t = 5 s . Substitute 5 s for t in Equation v = 2 π 5 cos ( π 5 t ) . v = 2 π 5 cos ( π 5 ( 5 ) ) = 2 π 5 ( − 1 ) = − 2 π 5 m/s When, t = 7

MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK

15th Edition

ISBN: 9780137519170

Author: HIBBELER

Publisher: PEARSON

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Chapter 12, Problem 39P

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The s−t , v−t and a−t graphs for the time interval 0≤t≤10 s .

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Chapter 12, Problem 38P

Chapter 12, Problem 40P

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MOD.MASTER.W/ETEXT ENG.MECHANICS CARD+BK

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To construct: The s − t , v − t and a − t graphs for the time interval 0 ≤ t ≤ 10 s .

Solution Summary: The author explains how to construct the s-t, v-, and a t graphs for the time intervals.

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To construct:

The s−t , v−t and a−t graphs for the time interval 0≤t≤10 s .

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Chapter 12 Solutions

To construct: The s − t , v − t and a − t graphs for the time interval 0 ≤ t ≤ 10 s .

Solution Summary: The author explains how to construct the s-t, v-, and a t graphs for the time intervals.

Concept explainers

Videos

To construct: The s−t , v−t and a−t graphs for the time interval 0≤t≤10 s .

Want to see the full answer?

Chapter 12 Solutions

To construct:

The s−t , v−t and a−t graphs for the time interval 0≤t≤10 s .