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# Differential Equations/Physics

Question
A motorist travelling at 13m/s approaches traffic lights which turn red when he is 25m away from the stop line. His reaction time is 0.7s. The condition of the road and his tyres is such that the car cannot slow down at more than 4.5m/s^2. If he brakes fully, how far from the stop line will he stop, and on whichside of it?

Take x= 0 as where the stop light is at.  This means that his current position is at -25.
Since the equation has a -a/2, and a=4.5, the equation for distance is
-25 + 13t with a -2.25t² when the time at least 0.7.

At t = .7, the position is -25 + 13(0.7) = -25 + 9.1 = -15.9.
He is still travelling at full speed at this point in time.
This makes the equation at this point forward to be -15.9 + 0.7t - 2.25t².

Since at the start he is going 13m/s and the deceleration is 2.25m/s².
That means the time at which he stops is at (13/4.5)s.

{ That is also {multiplying by 2/2} (26/9)s, which is almost 3 seconds }.

Letting t=26/9 in the equation -15.9 + 13t - 2.25t² gives

At around t=1.8, he has gone farther than the top sign, so he did not brake in time.

{by the way, the characters √ and ² are alt-251 and alt-253}

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Differential Equations

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#### Scott A Wilson

##### Expertise

I am capable of solving most ordinary differential equations and a few not so ordinary, but those are few and far between.

##### Experience

I have taken Differential Equations at OSU. Occasionally I have assisted people with questions on the subject.

Publications
I wrote a thesis on the study of shock waves and rarefaction fans. That occurs in nature when mathematics fails to apply. See, mathematics says that when shock waves appear, there should be two solutions whereas nature knows there is only one way to be in that area. When rarefaction fans occur, the mathematics says there should be no solution, but despite this, nature still moves ahead with its own plan.

Education/Credentials
I received an MS degree at OSU in Mathemematics and a BS degree at OSU in Mathematical Science.

Awards and Honors
I graduated from OSU with a Bachelor of Science degree in mathematics with honors. Two years later, I graduated from OSU with a Master of Science degree in mathematics with honors. Between these two degrees, I have more hours in graduate courses that required to get them.

Past/Present Clients
I answered many questions at OSU, down in south seattle at a college, at a church in Corvallis, OR, as Safeway in Washington, and many other areas. I have answered over 8,500 right here, but only a little over 190 of them have been in differential equations.