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To begin, it would be unethical to use this service to answer an exam question. If you're working a problem set it'd be okay.
As I understand the problem, a car traveling 55 mi/hr accelerates at a rate of 60 meters/second^2 to a speed of 60 mi/hr. How long did it take to reach the final speed?
I don't remember the formula for this, but I figured it out by looking at the units.
acceleration is in distance/time^2
time is in time
change in velocity is in distance/time
Only the change in velocity matters in this problem. So, 60mi/hr - 55mi/hr = 5 mi/hr
The time would be the same if the car started at zero and accelerated to 5 mi/hr.
Using these three values, the only way to equal a time unit is:
mi/hr x hr^2/mi = time in hr
or
m/s x s^2/m = time in s
This makes an equation of: (change in velocity)/acceleration = time
or
more commonly written: time x acceleration = velocity
The next step is to put all three values in the same units.
change in velocity = (5mi/hr)(5280ft/1mi)(12in/1ft)(2.54cm/1in)(1m/100cm) = 2.2352m/s
acceleration = 60 m/s^2
This will yield time in seconds.
So, plug and chug:
(2.2352m/s)/(60m/s^2) = time in seconds = 0.037253333s = 3.7 x 10^-2 s <-- significant figures
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This seemed fast to me, so I tried converting it the other way too:
acceleration = (60m/s^2)(100cm/1m)(1in/2.54cm)(1ft/12in)(1mi/5280ft)(60s/1min)^(2) (60min/1hr)^(2) = 483178.24mi/hr^2 = really really fast!
Therefore:
(5mi/hr)/(483178.24mi/hr^2) = time in hours = 1.034815 x 10^-5 hr = 1.0 x 10^-5 <-- significant figures
This is the same as 3.7 x 10^-2 seconds
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Keeping the units straight is the key.
To make sure you've got it, change the numbers and rework the problem.
