Answer:
It has moved a distance, S = 25.9 m
Explanation:
F = 40 v²........(1)
[tex]F = mv\frac{dv}{dS}[/tex].........(2)
Equating (1) and (2)
[tex]-mv\frac{dv}{dS} = 40 v^2\\\\v\frac{dv}{dS} = \frac{-40 v^2}{m} \\\\m = 450 kg\\v\frac{dv}{dS} = \frac{-40 v^2}{450}\\\\ \frac{dv}{v} = \frac{40}{450} dS\\[/tex]
Integrate both sides:
[tex]v_1 = 1, v_2 = 10[/tex]
[tex]\int\limits^{10}_1 {\frac{1}{v} } \, dv = \frac{-40}{450} \int\limits^S_0 \, dS \\\\ln\frac{1}{10} = \frac{-40}{450} (S-0)\\\\S = \frac{-40}{450} ln(0.1)\\\\S = 25.9 m[/tex].
