The a–s graph for a rocket moving along a straight track has been experimentally determined. If the rocket starts at s = 0 when v = 0, determine its speed when it is at s = 75 ft, and 125 ft, respectively. Use Simpson’s rule with n = 100 to evaluate v at s = 125 ft.

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[latex]0 \le s < 100 \ \int_{ 0 }^{ v } v\space dv = \int_{ 0 }^{ x } 5ds \ \frac { 1 } { 2 } { v }^{ 2 } = 5s \ v = \sqrt{ 10s } \ ext{At}\space s = 75ft, \quad\quad v = \sqrt{ 750 } = 27.4 ft/s \ ext{At}\space s = 100ft, \quad\quad v = 31.623 \ v\space dv = ads \ \int_{ 31.623 }^{ v } v\space dv = \int_{ 100 }^{ 125 } [5 + 6{ (\sqrt{ s } - 10) }^{ 5/3 } ds] \ \frac { 1 } { 2 } { v }^{ 2 }|_{ 31.623 }^{ v } = 201.0324 \ v = 37.4 ft/s[/latex]

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