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: 6,704 Thanks: 670  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: 2,142 Thanks: 726 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: 6,704 Thanks: 670  

Tags 
acceleration, constant 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Constant acceleration  hyperbola  Physics  1  March 15th, 2015 10:10 PM 
Magnitude of Acceleration  Rollsroyce  Algebra  1  November 16th, 2013 01:07 PM 
Circular Acceleration  yogazen2013  Physics  1  September 25th, 2013 09:35 PM 
acceleration  Mike7remblay  Physics  3  February 1st, 2012 06:48 PM 
acceleration?  imcutenfresa  Calculus  5  October 7th, 2009 02:51 PM 