Question

You are driving $65\mathrm{mi}/\mathrm{h}$ and take your eyes off the road for "just a second." What distance (in feet) do you travel in this time?

Short answer

The vehicle travels approximately 95.333 feet when the driver takes his/her eyes off the road for a second.

Step-by-step solution

Convert speed from mi/h to ft/s

To convert the speed from miles per hour (mi/h) to feet per second (ft/s), we need to multiply it by a conversion factor. We know that 1 mile = 5280 feet and 1 hour = 3600 seconds. Therefore, our conversion factor is $\frac{5280\mathrm{ft}}{1\mathrm{mi}}\times \frac{1\mathrm{hr}}{3600\mathrm{s}}$. Now, we'll multiply the given speed (65 mi/h) by this conversion factor: $65\frac{\mathrm{mi}}{\mathrm{h}}\times \frac{5280\mathrm{ft}}{1\mathrm{mi}}\times \frac{1\mathrm{hr}}{3600\mathrm{s}}$.

Simplify the expression

After multiplying, we need to simplify the expression: $65\frac{\cancel{\mathrm{mi}}}{\cancel{\mathrm{h}}}\times \frac{5280\mathrm{ft}}{\cancel{1\mathrm{mi}}}\times \frac{\cancel{1\mathrm{hr}}}{3600\mathrm{s}}$. Now the units are canceled out, and we have: $65\times \frac{5280}{3600}\frac{\mathrm{ft}}{\mathrm{s}}$.

Calculate the speed in ft/s

Now we can perform the multiplication to find the speed in feet per second: $65\times \frac{5280}{3600}\approx 95.333\frac{\mathrm{ft}}{\mathrm{s}}$. So, the speed of the vehicle in feet per second is approximately 95.333 ft/s.

Calculate the distance traveled in 1 second

Since we have the speed in ft/s and the time (1 second), we can now calculate the distance traveled by multiplying speed by time: Distance = Speed × Time Distance ≈ 95.333 ft/s × 1 s Distance ≈ 95.333 ft

Final answer

The vehicle travels approximately 95.333 feet when the driver takes his/her eyes off the road for a second.