A car of mass 997 kg coasts on a level road, starting with an initial speed of 1

Question

A car of mass 997 kg coasts on a level road, starting with an initial speed of 13.9 m/s and coming to rest 14.0 s later. Find the frictional force acting on the car. ???

(a) Find the maximum rate of deceleration of a car on a dry, level road, assuming the coefficient of static friction between tires and pavement equals 1.1.
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(b) Find the minimum stopping distance if the car has an initial speed of 22.9 m/s.
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(c) Repeat parts (a) and (b) assuming a wet, oily surface for which µs = 0.13. maximum rate of acceleration ???
minimum stopping distance ???

Explanation / Answer

According to equation's of motion,       v = u + at since final velocity is zero, acceleration, a= u/t = 13.9/14.0 = 0.992 m/s^2 the frictional force, f = ma                                    = 997*0.992                                    = 989.87 N ------------------------------------------- (a) the frictional force f = mg but the force f = ma therefore a = g ------------ (1)      a = 1.1*9.8 = 10.78 m/s^2 . (b) According to equations of motion, 0-v^2 = -2as a = v^2/2S ------------------ (2) From equation (1) and (2); S = v^2/2*g    (since = 1.4)     = 24.32 m the minimum stopping distance is 24.32 m. --------------- if the = 0.13 then (a) the deceleration, a = g = 1.274 m/s^2 (b) the distance S = v^2/2*g          S = 205.81 m

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