what should a do

Question

The speed of light in empty space — the ultimate speed limit of the Universe — is 9.45 x 10¹² km yr^-1. 

Answer 1

I'm guessing that you need to convert this speed to meters per second (ms^-1), which just requires a few steps of dimensional analysis.

We want to convert km yr^-1 to m s^-1, so first we convert km to m, which is simply:

1 km = 1000 m

or, we can create a conversion factor to cancel out km and replace it with m:

(1000 m)/(1 km)

Then we want to convert yr^-1 to s^-1, which you can either look up directly, or go through the steps:

1 yr = 365 d ⇒ (1 yr)/(365 d)

Again, we have yr/d to cancel out the year unit on the bottom, and replace it with the day unit on the bottom.

Moving forward, days to hours:

1 d = 24 hr ⇒ (1 d)/(24 hr)

Then, hours to minutes:

1 hr = 60 min ⇒ (1 hr)/(60 min)

Finally, minutes to seconds:

1 min = 60 s ⇒ (1 min)/(60 s)

Now, lastly, we combine all these conversion factors into one, giving us the unit conversion from km yr^-1 to m s^-1:

(m s^-1)/(km yr^-1) = [(1000 m)/(1 km)] × [(1 yr)/(365 d)] × [(1 d)/(24 hr)] × [(1 hr)/(60 min)] × [(1 min)/(60 s)]

= 1/31536 m s^-1km^-1 yr

Now, if we take this conversion factor and multiply it by the original speed of 9.45 x 10¹² km yr^-1:

(9.45 x 10¹² km yr^-1) x (1/31536 m s^-1km^-1 yr) = 299657534.24658 m s^-1

= 2.99658 x 10⁸ m s^-1 ≈ 3 x 10⁸ m s^-1

It's a bit lengthy here, just to show all the steps of converting units. As long as you can put the units in the right place, this becomes a very useful tool called Dimensional Analysis. While most people don't know the exact conversion between a year and seconds, you can find it yourself through this process. It can be used for any unit conversion where you know the intermediate, or "middle", units between the given unit and the unit you want to convert to.