Solve the Problem $a = d ^ { 2 } s / d t ^ { 2 } = ( 5 / \sqrt { t } ) + 9 \sqrt { t }$

question 8

Multiple Choice

Solve the problem.
-A particle moves on a coordinate line with acceleration $a = d ^ { 2 } s / d t ^ { 2 } = ( 5 / \sqrt { t } ) + 9 \sqrt { t }$ , subject to the conditions that $\mathrm { ds } / \mathrm { dt } = 3$ and $\mathrm { s } = 1$ when $\mathrm { t } = 1$ . Find the velocity $\mathrm { v } = \mathrm { ds } / \mathrm { dt }$ in terms of $\mathrm { t }$ and the position $s$ in terms of $t$ .

• A) \(v = 10 \sqrt { t } + 6 \sqrt [ 3 ] { t } - 13 ; s = \frac { 20 } { 3 } \sqrt [ 3 ] { t } + \frac { 12 } { 5 } \sqrt [ 5 ] { t } - 13 t + \frac { 74 } { 15 }\)
• B) \(v = 10 \sqrt [ 3 ] { t } + 6 \sqrt [ 3 ] { t } - 13 ; s = \frac { 20 } { 3 } \sqrt [ 5 ] { t } + \frac { 12 } { 5 } \sqrt [ 3 ] { t } - 13 t + \frac { 74 } { 15 }\)
• C) \(v = \frac { 20 } { 3 } \sqrt [ 3 ] { t } + \frac { 12 } { 5 } \sqrt [ 5 ] { t } - 13 t + \frac { 74 } { 15 } ; s = 10 \sqrt { t } + 6 \sqrt [ 3 ] { t } - 13\)
• D) \(v = 10 \sqrt { t } - 6 \sqrt [ 3 ] { t } + 13 ; s = \frac { 20 } { 3 } \sqrt [ 3 ] { t } - \frac { 12 } { 5 } \sqrt [ 5 ] { t } + 13 t + \frac { 74 } { 15 }\)

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