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Sagot :
We are given that a train is traveling at the following constant speed:
[tex]v=\frac{105\text{ miles}}{hour}[/tex]We are asked to determine the distance after 3 seconds. To do that, let's remember that speed is the ratio between distance and time, that is:
[tex]v=\frac{d}{t}[/tex]Where:
[tex]\begin{gathered} d=\text{ distance} \\ t=\text{ time} \end{gathered}[/tex]Since we want to determine the distance we will multiply both sides of the equation by "t":
[tex]vt=d[/tex]Now, we substitute the values:
[tex]\frac{105\text{ miles}}{hour}\times(3s)=d[/tex]Since the velocity is given per unit of hour, we need to convert the 3 seconds into hours. We do that using the following conversion factor:
[tex]1\text{hour}=3600s[/tex]Now we multiply the time by the conversion factor:
[tex]3s\times\frac{1h}{3600s}=\frac{1}{1200}h[/tex]Now we substitute in the formula for the distance:
[tex]\frac{105\text{ miles}}{hour}\times(\frac{1}{1200}hour)=d[/tex]Solving the operations:
[tex]\frac{7}{80}miles=d[/tex]Now, we convert the miles into feet using the given conversion factor:
[tex]1\text{mile}=5280\text{feet}[/tex]Now, we multiply by the conversion factor:
[tex]d=\frac{7}{80}\text{miles}\times\frac{5280feet}{1mile}[/tex]Solving the operations:
[tex]d=462feet[/tex]Therefore, the distance is 462 feet.
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