A car is moving with a velocity of 45 mi/hr. Calculate its velocity in the indicated units:
a) m min–1 b) mm cs–1 c) Mm/day d) in/s

Question

A car is moving with a velocity of 45 mi/hr.  Calculate its velocity in the indicated units: 
a)  m min–1	b)  mm cs–1	c)  Mm/day	d)  in/s

mathstudent55 · Answer

Do you know the conversion factor between the units you need to use?

anonymous · Answer

No i don't.

mathstudent55 · Answer

Then you need to find all the conversion factors.

lucaz · Answer

a) miles/min right?

mathstudent55 · Answer

1 in. = 2.54 cm
12 in. = 1 ft
5280 ft = 1 mi

1 day = 24 h
1 h = 60 mn
1 mn = 60 s
1 s = 100 cs

1 Mm = 1 000 000 m
1 m = 1000 mm
1 m = 100 cm

These are the conversion factors you need.

mathstudent55 · Answer

Each conversion factor can be written as a fraction that equals 1 in two different ways.

For example, we know that 
1 ft = 12 in.

Dividing both sides by 12 in., you get:

$ \dfrac{1~ft}{12~in.} = 1$

Starting with 1 ft = 12 in. again, dividing both sides by 1 ft, you get:

$ 1 = \dfrac{12~in.}{1~ft} $

With this you see that each conversion factor can be written two ways. Each way is equal to 1.

$\dfrac{12~in.}{1~ft} = \dfrac{1~ft}{12~in.} = 1$

Converting units is a matter of multiplying the given amount by the proper conversion factors until you get all the unwanted units to cancel out, and only the wanted units to remain. We can multiply numbers by the conversion factors because every conversion factor equals 1. The multiplicative identity propetry tells us that any number multiplied by is equal to itself.

The way you choose which conversion fraction you use is based on which units you want and which units you don't want.

mathstudent55 · Answer

Here's how you do part a.
You have mi/h, and you want m/mn

$ 45 \dfrac{mi}{h} \times \color{red}{\dfrac{5280 ~ft}{1~mi} \times \dfrac{12~in}{ 1~ft} \times 
\dfrac{2.54~cm}{1~in.} \times \dfrac{1~m}{100~cm}} \times \color{blue}{\dfrac{1~h}{60~mn}}$

The given information is in black. 
The conversion factors from miles to meters are in $ \bf \color{red}{red} $.
The conversion factors from hours to minutes are in $ \bf \color{blue}{blue} $.

Now you need to multiply out the entire expression and cancel out units and make sure you get the desired units at the end.