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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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