Explanation Given: The Equation of the velocity of the particle at s = 0 is v = ( t 2 − 4 t + 3 ) m/s . Write the given equation of velocity ( v ) of the particle. v = ( t 2 − 4 t + 3 ) m/s (I) Here, t is the time in seconds. Write the formula for acceleration ( a ) of the particle. a = d v d t (II) Here, d v d t is rate of change of velocity with respect to time. Conclusion: Calculate the velocity of the particle at the time interval of 0 s ≤ t ≤ 4 s . When, t = 0 s . Substitute 0 s for t in Equation (I). v = ( t 2 − 4 t + 3 ) m/s = [ ( 0 ) 2 − 4 ( 0 ) + 3 ] = 3 v | t = 0 s = 3 m/s When, t = 1 s . Substitute 1 s for t in Equation (I). v = ( t 2 − 4 t + 3 ) m/s = [ ( 1 ) 2 − 4 ( 1 ) + 3 ] = 1 − 4 + 3 v | t = 1 s = 0 m/s When, t = 2 s . Substitute 2 s for t in Equation (I). v = ( t 2 − 4 t + 3 ) m/s = [ ( 2 ) 2 − 4 ( 2 ) + 3 ] = 4 − 8 + 3 v | t = 2 s = − 1 m/s When, t = 3 s . Substitute 3 s for t in Equation (I). v = ( t 2 − 4 t + 3 ) m/s = [ ( 3 ) 2 − 4 ( 3 ) + 3 ] = 9 − 12 + 3 v | t = 3 s = 0 m/s When, t = 4 s . Substitute 4 s for t in Equation (I). v = ( t 2 − 4 t + 3 ) m/s = [ ( 4 ) 2 − 4 ( 4 ) + 3 ] = 16 − 16 + 3 v | t = 4 s = 3 m/s Plot the v − t graph for the interval of 0 s ≤ t ≤ 4 s as shown in Figure (1)

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

15th Edition

ISBN: 9780137519170

Author: HIBBELER

Publisher: PEARSON

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Chapter 12, Problem 38P

To determine

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The v−t and a−t graphs for the time interval 0≤t≤4 s .

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Chapter 12, Problem 37P

Chapter 12, Problem 39P

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