Question

How do you convert 3.82 meters per second to kilometers per hour?

Answer 1

See a solution process below:

Explanation:

First, we can write this expression as:

`(3.82"m")/"sec"`

Next, let's convert the seconds to hours. We know 1 minute is equal to 60 seconds and 1 hour is equation to 60 minutes so we can write multiply this expression by `1` twice without changing the value of the expression:

`(3.82"m")/"sec" xx (60"sec")/(1"min") xx (60"min")/(1"hr") =>`

`(3.82"m")/color(red)(cancel(color(black)("sec"))) xx (60color(red)(cancel(color(black)("sec"))))/(1color(blue)(cancel(color(black)("min")))) xx (60color(blue)(cancel(color(black)("min"))))/(1"hr") =>`

`3.82"m" xx 60 xx 60/(1"hr") =>`

`(13752"m")/(1"hr")`

Now, let's convert meters to kilometers. We know 1 kilometer is equal to 1000 meters. So again, we can multiply the expression by 1 without changing the value of the expression:

`(13752"m")/(1"hr") xx (1"km")/(1000"m") =>`

`(13752color(red)(cancel(color(black)("m"))))/(1"hr") xx (1"km")/(1000color(red)(cancel(color(black)("m")))) =>`

`13752/(1"hr") xx (1"km")/1000 =>`

`(13752"km")/(1000"hr") =>`

`(13.752"km")/"hr"`

Answer 2

`13.752" Km per hour"`

Explanation:

`"convert metres to Km and seconds to hours"`

`• " 1 Km "=1000" metres"`

`• " 1 hour " =60xx60=3600" seconds"`

`rArr3.82" metres per second"`

`=3.82/1000" Km per second"`

`=3.82/1000xx3600" Km per hour"`

`=13.752" Km per hour"`

Answer 3

`"3.82 m/s"` equals `"13.75 km/h"`.

Explanation:

Use dimensional analysis.

Identify the relationships between km and m and seconds and hours.

`"1 km = 1000 m"`

`"1 h = 3600 s"` `larr` Multiply `"60 min"` by `("60 s")/("min")`

Multiply `"3.82 m"/"s"` by the two conversion factors that will cancel meters and seconds and leave km/h.

`(3.82color(red)cancel(color(black)("m")))/(color(red)cancel(color(black)("s")))xx(1"km")/(1000color(red)cancel(color(black)("m")))xx(3600color(red)cancel(color(black)("s")))/(1"h")="13.75 km/h"`