How do I convert 6.7 km/hr/sec to m/sec^2

[Lia44]

1. Convert 6.7 km/hr/sec to m/sec^2.
I was given the initial value and the units (kilometers/hour/seconds) to (meters/seconds squared).

2. image for clarification

3. The correct answer is 1.89 m/s^2. I watched a video on how to do it (and followed the video to get the following), but I don't understand why I can write the initial value as 6.7km/(hr*s), as shown in the following image.

 

[berkeman]

Wowie! Giant images.

A good way to do unit conversions is to keep multiplying by "1" and cancelling units. Start by multiplying by 1=1hr/3600s.

Can you carry on from there?

 

[berkeman]

Actually, that is shown in your post of the hint/solution. Do you understand how multiplying by "1" doesn't change the overall value, but gives you the opportunity to start cancelling units to make the conversions?

 

[collinsmark]

Hello @Lia44,

Welcome to Physics Forums!

Another trick you'll want to memorize is when dividing two fractions, say \frac{a}{b} divided by \frac{c}{d},

\frac{\left( \frac{a}{b} \right) }{\left( \frac{c}{d} \right)} = \frac{a}{b} \cdot \frac{d}{c}

Notice how when \left( \frac{c}{d} \right) is brought to the top, the numerator and denominator are flipped to form \left( \frac{d}{c} \right). [Edit: Technically, this is accomplished by multiplying both the numerator and denominator of the big fraction by \frac{d}{c}. Then the denominator of the big fraction reduces to "1" and doesn't require notation.]

Now what happens if instead, there is no d? Suppose we just have \frac{a}{b} divided by c?

\frac{\left( \frac{a}{b} \right) }{c} = \ ?

Well, c is the same thing as \frac{c}{1}, so we have

\frac{\left( \frac{a}{b} \right) }{c} = \frac{\left( \frac{a}{b} \right) }{ \left( \frac{c}{1} \right)} = \frac{a}{b} \cdot \frac{1}{c} = \frac{a}{bc}