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\int_{0}^{5} \mathrm{v}_{\mathrm{A}}(t)-\mathrm{v}_{\mathrm{b}}(t) \mathrm{dt}=\frac{5}{2} t^{2}-\left.\frac{t^{3}}{3}\right|_{0} ^{5}=20 \frac{5}{6} \text { meters. }