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The acceleration of a particle traveling along a straight line is a \frac { 1 } { 2 }{ s }^{ 1/2 }m/{ s }^{ 2 }, where s is in meters. If v = 0, s = 1 m when t = 0, determine the particle’s velocity at s = 2 m.

Step-by-step

Velocity:

\begin{aligned}(+ \downarrow)\quad\quad & v\space dv = a\space ds \\ & \int_{ 0 }^{ v } { v\space dv } = \int_{ 1 }^{ s } \frac { 1 } { 4 } { s }^{ 1/2 }ds \\ & \frac{ { v }^{ 2 } }{2}|_{ 0 }^{ v } = \frac { 1 } { 6 } { { s }^{ 3/2 } }|_{ 1 }^{ s } \\ & v = \frac{ 1 } { \sqrt{ 3 } } { { ({ s }^{ 3/2 } – 1) }^{ 1/2 }m/s } \end{aligned}

When s = 2 m, v = 0.781 m/s.

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