An automobile is traveling on a long, straight highway at a steady 75.0 m/h when

Question

An automobile is traveling on a long, straight highway at a steady 75.0 m/h when the driver sees a wreck 170 m ahead. At that instant, she applies the brakes (ignore reaction time). Between her and the wreck are two different surfaces. First there is 140 m of ice, where the deceleration is only 1.20 m/s^2 . From then on, it is dry concrete, where the deceleration is a more normal 7.90 m/s^2 .

What was the car’s speed just after leaving the icy portion of the road?

What is the total distance her car travels before it comes to a stop?

What is the total time it took the car to stop?

Explanation / Answer

75.0 mi/h = 33.52800 m/s a) On ice v^2 = (33.528)^2 - 2(140) = 844.127 answer v = 29.05 m/s On concrete (29.05)^2 = 0 - 2(7.9)x 843.9/ 15.8 = x = 53.41 meters b) 140 +66 = 206 meters c) t(ice) = 33.52 - 29.05 = 4.47s on concrete 29.05 -7.9t = 0 t = 3.68 s Total time = 4.47 + 3.67 = 8.15 seconds

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