Answer:1.8 hr
Explanation:
Given
mass of cargo=500,000 kg
initial speed[tex]=75 km/h\approx 20.833 m/s[/tex]
Frictional force=85 v
at t=0 engine is shut off so acquired speed is slowly decreasing
[tex]85v=-500,000\frac{\mathrm{d} v}{\mathrm{d} t}[/tex]
[tex]85dt=-\frac{dv}{v}[/tex]
Integrating both sides
[tex]85\int_{0}^{t}dt=-500,000\int_{20.83}^{6.944}\frac{dv}{v}[/tex]
[tex]85t=500,000\ln \frac{1}{3}[/tex]
t=6462.425 s
t=1.8 hr
