An Automobile is traveling on a long, straight highway at a steady 76.0 mi/h whe

Question

An Automobile is traveling on a long, straight highway at a steady 76.0 mi/h when the driver sees a wreck 180m ahead. At that instant, she applies the brakes. between her and the wreck are two different surfaces first there is 130m of ice, where the deceleration is only 1.20 m/s2. From then on, it is dry concrete, where the deceleration is a more normal 7.10 m/s2

A. What was the cars speed just after leaving the icy portion of the road?

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

C. What is the total time it took the car to strop?

Explanation / Answer

a) Initial speed of car = u = 76.0 mi/h = 33.97504 m / s

Distance travelled on ice = s =130 m

deceleration = -1.2 m/s2

Let final speed be v

v2 = u2 + 2 * a * s

v2 = 33.972 - 2 * (1.2) * 130

v2 = 1153.96 - 312 = 841.9609

v = 29.01 m/s

b) Now the car travels on concrete.

Initial speed = 29.01 m/s

Final speed = 0 m/s (since it stops)

Deceleration = 7.1 m/s2

v2 = u2 + 2 * a * s

0 = 29.012 - 2 * 7.1 * s

s = 59.29 m

Hence total distance travelled before stopping = 130 + 59.29 = 189.29 m

c) For ice, v = u + at

or, 29.01 = 33.97 - 1.2*t

t = 4.133 seconds

For concrete, v = u + at

0 = 29.01 - 7.1 * t

t = 4.086 seconds

Total time taken = 4.133 + 4.086 = 8.219 seconds

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