Question

154mi/h = ____ in/s

Please explain step by step.

Answer 1

2710.4 in/s

Explanation:

You want to convert a speed of 154 miles per hour to one in inches per second.

Unit conversion

Dimensions can be converted by multiplying by a factor that has a value of 1, but dimensions chosen to cancel ones you don't want and leave ones you do want.

Application

We know that ...

1 mi = 5280 ft

1 ft = 12 in

1 h = 3600 s

So, we can convert the speed like this:

`\frac{154\text{ mi}}{\text{h}}=\frac{154\text{ mi}}{\text{h}}*\frac{5280\text{ ft}}{\text{mi}}*\frac{12\text{ in}}{\text{ft}}*\frac{1\text{ h}}{3600\text{ s}}\\\\=(154*5280*12)/(3600)\,\frac{\text{in}}{\text{s}}=\boxed{2710.4\text{ in/s}}`

__

Note that each of the ratios ((5280 ft)/(1 mi), for example) has the same amount in the numerator as in the denominator. This means the value of the ratio is 1. Multiplying by this ratio only has the effect of changing the units. It does not change the speed.