Physics Equation Question?

Question

I am doing a physics problem that requires me to find if a car was speeding or not. This is the information i was given:
&bull;	Involved two cars: A yellow car and a red car
&bull;	The manufacturers of the cars say the yellow car model has a weight of 9810 N and the red car model has a weight of 24,525 N
&bull;	The yellow car was at a stoplight when it was hit from behind by the red car 
&bull;	Tire skid marks first appear 30 meters behind the stoplight
&bull;	Two sets of skid marks appear after the light and travel for 12.25 meters
&bull;	The speed limit of this road is 45 miles per hour
&bull;	A city engineer confirms that the coefficient of friction of the asphalt road is 0.7
&bull;	A nearby high speed traffic cam captured the collision on film. The time stamps show it took 1.4 seconds between the time the red car begin decelerating and hitting the yellow car 

I have the velocity equaling 21.43 m/s, but I don't know where to go from there. Help please?

Answer

Hello, this is a fascinating question, I admit. Took me entire lunch time to solve it. The question involves motion in one dimension and conversion of momentum. First, I start with the part two cars hit and stop, which is after the stoplight. I use the formula: Vf^2 - Vi^2 = 2ax (acceleration times distance). Knowing that two cars have completely stopped at the end, Vf = 0. So, the equation becomes 2(12.25m)a + Vi^2 = 0. Then, I use -a=&mu;g to calculate acceleration. Just in case you don't know how I got the equation, because there is no force exerts on the objects, the Ff = -F. And Ff=&mu;mg and F= am. So, -a =&mu;g = -0.7(9.81m/s^2) = -6.867m/s^2. Vi=12.97 m/s. Because P red (momentum of the red car) = P tot (momentum of the total), mv red = mv tot.  (24525N/9.81m/s^2) * V red= (24252N/9.81m/s^2 + 9810N/9.81m/s^2) * 12.97m/s.  V red = 18.158m/s. Finally, we need to calculate the initial speed of the red car and use the formula: (Vi+Vf)/2 * t= x.   (18.158m/s + Vi)/2 * (1.4s) = 30m.   Vi=24.7m/s = 55.6mile/hour. Since the speed limit is 45miles per hour, the red car was speeding.

Physics Equation Question?

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