Fine. You just need a conversion at some point between seconds and hours.
Let's do it this way:
First, let's review one very useful definition of acceleration:
Acceleration = (change in speed) / (time for the change)
The question is asking for a time, so let's massage this equation to get
time all by itself.
Multiply each side by (time for the change) :
(Acceleration) x (time for the change) = (change in speed)
Divide each side by (acceleration) :
Time for the change = (change in speed) / (acceleration).
There it is. The problem gives you the change in speed and the acceleration.
Change in speed = (110 - 80) = 30 km/hr
Acceleration = 1.6 m/s²
Here's where the only difficulty shows up. One is in hours and the
other one is in seconds.
The way you change the units of a quantity is to multiply it by
a fraction whose value is ' 1 '. That way you don't change the value
of the original quantity.
How does that help ? You just pick the fraction very carefully ! Remember
that the value of a fraction is ' 1 ' if the numerator and denominator are both
the same value. Here are some fractions that are equal to ' 1 ' :
12 inches/1 foot 60 seconds/1 minute 1 meter/100 centimeters
See how that works ? Multiply one of these by a quantity, and it changes
the units of the quantity, but not its value.
Let's change 1.6 m/s² to m/hr² .
1 hour = 3,600 seconds so the fraction is (3600 sec/hr) .
The unit conversion is: (1.6 m/s²) x (3600 sec/hr) x (3600 sec/hr)
I multiplied by the fraction twice because we need sec² on top to cancel
the s² on the bottom.
Multiply this out and you get 20,736,000 m/hr².
Don't let the big number scare you.
Now go back to our equation for the time:
Time for the change = (change in speed) / (acceleration)
Change in speed = 30 km/hr
Acceleration was 1.6 m/sec² but we found that
that's the same as 20,736,000 m/hr² .
And also, since the change in speed is in km,
let's change this one to 20,736 km/hr² .
Time for the change = (30 km/hr) / (20,736 km/hr²)
30 / 20,736 = 0.0001447 hour
= 5.2 seconds.
I realize that this has turned into a nightmare. I probably lost you, and
the answer is likely wrong because the numbers got so ugly. I apologize.
The reason for all the ugly numbers is that I apparently picked the wrong
number to change the units. It probably would have been a lot neater to
convert the change in speed to m/sec instead of changing the acceleration
to m/hr² . But the principle is the same. Make a fraction out of the unit you
have and the new unit you want, wit the same value on top and bottom, and
use it to convert the units of one number to match the units of the others.
========================================
Change in speed = (30 km/hr) x (1000 m/km) x (1 hr / 3600 sec) = 8.333 m/sec
Time = (change in speed) / (acceleration) = (8.333 m/s) / (1.6 m/s²) = 5.2 seconds
Yes, this way was certainly better and prettier.
But at least I got the same answer going the long tough way!
