Explanation An object experiences linear acceleration given by, a ( t ) = ( 2 t + 1 ) ft/s 2 . The above equation can also be written as, d v d t = ( 2 t + 1 ) ft/s 2 d v = ( 2 t + 1 ) d t Now integrate on both sides, we get ∫ d v = ∫ ( 2 t + 1 ) d t v = 2 ( t 2 2 ) + t + C v = t 2 + t + C The object starts its motion ( at t = 0 ) at s = 4 with initial velocity 2 ft/s , then 2 a s = v 2 − u 2 2 ( 2 t + 1 ) ( 4 ) = v 2 − ( 2 ) 2 16 t + 8 + 4 = v 2 ± 16 t + 12 = v Thus, v = t 2 + t + C 16 t + 12 = t 2 + t + C 16 ( 0 ) + 12 = ( 0 ) 2 + ( 0 ) + C 12 = C So, the velocity of the object is v = t 2 + t + C v ( t ) = t 2 + t + 12 ft/s Now, d s d t = ( t 2 + t + 12 ) d s = ( t 2 </

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 5, Problem 72SP

To determine

To calculate: The velocity and position of the object, given that it starts its motion ( at t=0 ) at s=4 with initial velocity 2 ft/s .

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Chapter 5, Problem 71SP

Chapter 5, Problem 73SP

Chapter 5 Solutions

Calculus

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The velocity and position of the object, given that it starts its motion ( at t = 0 ) at s = 4 with initial velocity 2 ft/s .

Solution Summary: The author calculates the velocity and position of the object, given that it starts its motion at t=0 with initial velocity 2ft/s.

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To calculate: The velocity and position of the object, given that it starts its motion ( at t=0 ) at s=4 with initial velocity 2 ft/s .

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Chapter 5 Solutions