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

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