Melissa H.

asked • 05/05/17

How far to accelerate 0 to 75 mph?

Can a normal car like 2004 Toyota Corolla actually accelerate 0 to 75 mph in only .5 mile distance?

Patrick D.

If I may critique my own answer, rumors are the formula I used , in absence of time data, applies to circular motion rather than linear. Can any physics majors out there confirm or deny this and additionally what formula applies ? From a practical point of view consider the scenario of entering the freeway or interstate. You must accelerate while on the on-ramp entrance to meet the demands of the traffic flow. Most interstates and freeways have a speed limit of 70mph but comparable to the stated problem. The length of the on-ramp or entrance ramp is not exactly equal to a half mile but comparable to the stated problem. The only main difference between this problem and the scenario I am describing is that when merging onto the interstate, you are already traveling at a feasible speed. So consider the following comparable question: You are parked at the base of the entrance on-ramp of your local freeway or interstate. Is it possible from the instant as soon as you shift gears from "park " to "drive" to accelerate to 75 mph at the end of the on ramp and merge onto the interstate safely? I suppose there are some cars that can. I question if your typical car can. Mine can't. DON'T YOU DARE TRY THIS ON I4 my fellow Floridian!
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05/07/17

Patrick D.

Of course, some specialty cars are designed to do it, like race cars traveling at 200mph or faster for extended periods of time. The Lamborghini, etc But your typical, normal car, as you asked. If so, there may be repercussions. DON'T YOU DARE!
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05/08/17

Arturo O.

Patrick,
 
I am a physics major, and I confirm that your formula is correct.  It comes from kinematics in one dimension.  For constant acceleration, the distance d traveled under constant acceleration a is related to the initial and final speeds vi and vf by
 
vf2 - vi2 = 2ad
 
Starting from rest,
 
vi = 0
 
Then 
 
vf2 = 2ad ⇒ a = vf2 / (2d)
 
which is the equation that you used.
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05/08/17

1 Expert Answer

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Patrick D. answered • 05/06/17

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A = v^2/(2d) = (75*75)/(2*0.5) = 5625 miles per hour^2
 
they will not survive
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Arturo O.

It is good to convert the acceleration to feet/sec2:
 
5626 miles/hour2 = (5626 miles x 5280 feet/mile) / (1 hour x 3600 sec/hour)2 ≅ 2.29 feet/sec2 
 
This is less that 1g (g = 32 feet/sec2), so it appears a healthy human should survive it.  But to fully answer the question, we need more information, such as the maximum acceleration of the car, so we can compare the answer for "a" above to the maximum possible acceleration of the car.
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05/06/17

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