Explanation Given: The equation velocity of the projectile is v = 1800 ( 1 − e − 0.3 t ) mm/s . Initially the projectile is at origin s 0 = 0 . Write the formula for velocity of the projectile. v = d s d t d s = v d t (I) Here, v is the velocity, d s is the change in displacement and d t is the change in time. Conclusion: Calculate the position of the particle at the time t = 3 s . Substitute 1800 ( 1 − e − 0.3 t ) for v in equation (I). d s = [ 1800 ( 1 − e − 0.3 t ) ] d t Integrate at the limits s = 0 to s and t = 0 to t . ∫ 0 s d s = ∫ 0 t [ 1800 ( 1 − e − 0.3 t ) ] d t [ s ] 0 s = 1800 ∫ 0 t ( 1 − e − 0

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ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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Chapter 12, Problem 3RP

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The displacement of the projectile during the first 3 s .

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The displacement of the projectile during the first 3 s .

Solution Summary: The author calculates the position of the particle at the time t=3.

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