Convert 52.4 miles per hour to its equivalent in meters per second. Use dimensional analysis and show your work. Remember your significant figures!

Answer 1

Hello, Alexis,

Do you have conversion factors for miles and meters? Please add the required information when asking a question. I don't have your starting point for converting meters and miles, so I'll make it easy for me by selecting this conversion:

1 meter = 6.21x10^-4 mile

I can divide one side by the other to give either meters/mile or miles/meter. I'll select meters/mile:

1 = (1 meter/)(6.21x10^-4 mile), or

1 = 1.61x10³ meters/mile

Since the left side is 1, we can multiply this unit times anything and it will be numerically equivalent (valid) but now with units changed to meters instead of miles.

You can make equivalencies into conversion factors by dividing one side by the other. (e.g. 12 inches = 1 foot. So we can say either 1=(12in/ft), or 1= (1ft/12in).

Since I dislike division, I'll divide in a manner that I can multiply each step in the conversions, instead of divide. But if you love to divide, do the opposite.

Let's convert 50 miles/hr to meters/hr:

(50 miles/hr)*(1.61x10³ meters/mile) = 8.05x10⁴ meters/hr

The miles cancel, leaving meters/hr. We travel 8.05x10⁴ meters in one hour.

We want seconds instead of hours in the final value:

The conversion factors for getting there include:

60 sec = 1 minute

60 minutes = 1 hour

I want to convert meters/hr to meters/sec. We(I) want a conversion factor that is in hr/sec, so that I can multiply it times the above value in meters/hr and cancel out the hours, leaving minutes.

Putting seconds in the denominator: 1 = (1minute)/(60seconds)

Now I want to eliminate both hours and minutes, so let's take the second conversion and state it like this:

1 = (1 hour/60 minutes)

We left off with the distance conversion with:

8.05x10⁴ meters/hr

So let's arrange the time conversion factors so that all time units cancel, except for seconds:

(8.05x10⁴ meters/hour)*(1 hour)/(60 minutes)*(1 minute/60 seconds)

Let's cancel the units and see if we wind up with meters/hour:

(8.05x10⁴ meters/hour)*(1 hour)/(60 minutes)*(1 minute/60 seconds)

We are left with

(8.05x10⁴ meters)*(1/60)*(1/60 seconds) = 22.4 meters/sec

We started with 3 sig figs, so we report the answer with 3 sig figs, also. I leave more digits in during the calculations to insure there are no rounding errors. It is OK to leave them in until you report the final answer.

Bob