Adriver enters a one-lane tunnel at 34.4 m/s. the driver then observes a slow-moving van 154 m ahead travelling (in the same direction as the car) at a constant 5.65 m/s. the driver applies the brakes (ignore reaction time)of the car but can only accelerate at -2.00 m/s2 because the road is wet. how fast are you moving when you hit the rear of the van?
(a) 16.3 m/s
(b) 22 m/sec
(с) 4 m/sec
(d) 0 m/s

Ans. B) 22 m/s (the closest to what I have which was 20.16 m/s)

Explanation:

Hi, well, first, we have to find the equations for both, the driver and the van. The first one is moving with constant acceleration (a=-2m/s^2) and the van has no acceletation. Let´s write down both formulas so we can solve this problem.

or by rearanging the drivers equation.

Now that we have this, let´s equal both equations so we can tell the moment in which both cars crashed.

To solve this equation we use the following formulas

Where a=1; b=-28.75; c=154

So we get:

At this point, both answers could seem possible, but let´s find the speed of the driver and see if one of them seems ilogic.

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This means that 21.63s will outcome into a negative speed, for that reason we will not use the value of 21.63s, we use 7.12s and if so, the speed of the driver when he/she hits the van is 20.16m/s, which is closer to answer  A).

Best of luck