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This week's Challenge Question:
You are traveling at 40 miles per hour in your old Camaro and hit the brakes to stop your car. The Camaro stops after traveling 50 feet. Now you are traveling in the same road at 75 miles per hour. There is an intersection at 150 feet ahead of you whose traffic light just turned red. You hit the brakes. Would you be able to stop in time, or would you get a speeding ticket?
And the Answer is...
The stopping distance is determined by the force of friction between the road and the tires of the car. The force of friction produces the Work to change the velocity of the vehicle, according to the work-energy equation
In the above equation Fd is the friction work; d is the distance that this friction force is applied (the stopping distance), vo is the initial speed, or the speed at the moment of pushing the brake, v is the final velocity, and m is the mass of the car. If the car stops then v = 0. Solving for d in this equation yields
The negative sign indicates that as a consequence of applying the friction force the speed diminishes. It is clear that the stopping speed is directly proportional to the square of the initial speed. The quantities m and F are constants for this situation.
To calculate the stopping distance when you travel at 75 mph let's write a ratio using the two speed and solve for the second distance, as follows
Substitute d1=50, v1 = 40, and v2 = 75 to get
d2 = 175.8 feet.
Certainly, you will get a speeding ticket!
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