A car is being driven along a country road on a dark and rainy night at a speed

Question

A car is being driven along a country road on a dark and
rainy night at a speed of 20 m/s. The section of road is
horizontal and straight. The driver sees that a tree has fallen
and covered the road ahead. Panicking, the driver locks the
brakes at a distance of 20 m from the tree. If the coefficient
of friction between the wheels and road is 0.8, determine the
outcome.
a) The car stops 5.5 m before the tree.
b) The car stops just before reaching the tree.
c) As the car crashes into the tree, its speed is 18 m/s.
d) As the car crashes into the tree, its speed is 9.3 m/s.
e) This problem cannot be solved without knowing the mass of
the car.

The correct answer is D, but I keep getting the final velocity as 20.4 m/s. How did this come to a conclusion of 9.3 m/s?

Explanation / Answer

Given Intial velocity of car u = 20 m/s coefficient of friction between the wheels and road is =0.8 Distance x= 20 m ------------------------------------------------------------------------------- From Newton's second law,           ma =- mg The acceleration of the car is               a =- g                  =- (0.8)(9.80 m/s2)                  = -7.84 m/s2 From the kinematic relations,           v =[u2 +2ax]
             =[( 20 m/s)2 +2(-7.84 m/s2)(20 m)]              = 9.295 m/s               = 9.30 m/s So the correct answer is As the car crashes into the tree, its speed is 9.3 m/s. Therefore, the option (D) is correct.

              = 9.30 m/s So the correct answer is As the car crashes into the tree, its speed is 9.3 m/s. Therefore, the option (D) is correct.

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