## Question:

The as 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.

## Step-by-step

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