Since the stopping distance, from conservation of energy, is proportional to the
ID: 1527112 • Letter: S
Question
Since the stopping distance, from conservation of energy, is proportional to the square of the speed of the car, if you double the speed of a car the stopping distance becomes four times as great. Yet, the rule of thumb in many driver manuals is that a safe following distance behind another car is one car length for each 10 miles per hour you are traveling. But that formula would mean that the distance would only double if you doubled your speed. How do you reconcile these two different formulas for stopping distances. THIS IS A DIFFICULT QUESTION BUT UNDERSTANDING IT COULD SAVE YOUR LIFE! And, if you can explain this you will have a much greater insight into conservation of energy, velocity and acceleration. HINT: Your car doesn't start slowing down the instant you see a need to stop. You must first apply the brakes. What happens while you are applying the brakes?
Explanation / Answer
this can be explained by the concept of reaction time as human being has reaction time of 0.25 seconds. Reaction time means time our brain takes to react to decide the action when something odd happens.
so when a person is driving and sees a emergency of applying brakes, he does not instantly apply brakes but takes reaction time of 0.25 s to decide whether to apply brake or not.
so distance travelled by car before a driver apply brakes = 0.25 × v
so doubling the speed,v the distance to react also becomes double. thats why in many driver manuals is that a safe following distance will double on doubling distance.
and stopping distance is proportional to square of speed of car remains valid when he applies brakes so conservation of energy(K.E= Work done) is valid there.