May 11th, 2015, 06:26 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Constant Acceleration
A racing car is travelling at $130$ mph when the driver sees a brokendown car on the track $\frac{1}{10}$ of a mile ahead. Slamming the brakes on he achieves his maximum deceleration of $24.5$ mph per second. How far short of the brokendown car does he stop? My attempt, I know $u=130$, $a=24.5$, which formula should I use to solve this question? 
May 11th, 2015, 04:07 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  Quote:
First convert a to use one unit for time (hour  using mixed makes things complicated). Get time (t) from uat=0. then get distance (s) from $\displaystyle s=ut\frac{at^2}{2}$.  
May 12th, 2015, 04:53 AM  #3 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
I can't get the answer after figuring very long time. The answer is 0.0042 miles. How to convert 24.5 mph per second to 25.5 miles/h^2? Last edited by jiasyuen; May 12th, 2015 at 05:04 AM. 
May 12th, 2015, 05:20 AM  #4 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,156 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Using mixed units can be confusing, but I think this one isn't too bad. It's a good rule of thumb to convert to SI when you begin. If you find that you've already performed a bunch of calculations and you don't want to redo everything, then go back over your calculations and check the units at each step. Below is an example where the units have been considered at every calculation step. initial speed = u = 130 mph final speed = v = 0 mph acceleration = a = 24.5 mph /s Let's get the time taken to stop: SUVAT equation: $\displaystyle v = u+at$ $\displaystyle t = \frac{vu}{a} = \frac{0130}{24.5} = \frac{130}{24.5} = 5.306$ s This is in seconds because we have $\displaystyle [t] = \frac{mph}{(mph/s)}=\frac{mph \cdot s}{mph} = s$ Now we know the time taken to stop, we can get the distance travelled by the car as it's stopping: SUVAT equation: $\displaystyle s = ut + \frac{1}{2}at^2$ $\displaystyle = 130 \times 5.306  \frac{24.5}{2}(5.306)^2$ $\displaystyle = 689.796  344.898$ $\displaystyle = 344.898$ but what are the units of this? We have $\displaystyle [s] = mph \cdot s = \frac{miles \cdot s}{hr}$ miles seconds per hour? Lovely. Let's convert the hours into seconds. We know that there are 3600 seconds in an hour, so $\displaystyle 1 \frac{miles \cdot s}{hr} = 1 \frac{miles \cdot s}{3600 s} = \frac{1}{3600} \frac{miles \cdot s}{s} = \frac{1}{3600} miles$ So $\displaystyle = 344.898 mph \cdot s = \frac{344.898}{3600} miles = 0.0958 miles$ So the distance, $\displaystyle d$, between the broken down car and the speeding car is: $\displaystyle d = 0.1  0.0958 = 0.0042 miles$ Last edited by Benit13; May 12th, 2015 at 05:23 AM. 
May 12th, 2015, 05:52 AM  #5 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 
Benit. Thanks for your explanation.

May 12th, 2015, 06:31 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,770 Thanks: 700  

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