You are traveling along a road at 90km/hr, maintaining a constant distance d bet

Question

You are traveling along a road at 90km/hr, maintaining a constant distance d between you and the car infront of you, measured from your front bumper to the other car'srear bumper.

(a) If the driver of the car in front of youapplies the brakes to come to a complete stop, what is the minimumvalue of d required if you are not to hit the other car? Assumeyour reaction time (the time it takes you to see the brake lightsin front and apply your own brakes) is 0.36 s and that the appropriate coefficient offriction between the road and your car tires is 0.99. Assume the acceleration due to gravity has amagnitude of 9.8 m/s2.

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(b) What is the distance between the two cars at the instant youapply the brakes?
m (a) If the driver of the car in front of youapplies the brakes to come to a complete stop, what is the minimumvalue of d required if you are not to hit the other car? Assumeyour reaction time (the time it takes you to see the brake lightsin front and apply your own brakes) is 0.36 s and that the appropriate coefficient offriction between the road and your car tires is 0.99. Assume the acceleration due to gravity has amagnitude of 9.8 m/s2.

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(b) What is the distance between the two cars at the instant youapply the brakes?
m

Explanation / Answer

(a)    Initial Velocity of each car, U = 90km/h                                                 =90 * ( 5/18 ) m/s                                                = 25 m/s    Final velocity of each car , V = 0 m/s    Reaction time, t = 0.36 s        Acceleration, a = - g = - 0.99 * 9.8= - 9.702 m/s^2    Stopping distance = S    V2 - U2 = 2 a S    0 - 625 = 2 * - 9.702 * S    Stopping distance, S = 32.21 m    Distance travelled during the reaction time,X = U t                                                                            =25 * 0.36                                                                       = 9 m (a)    Minimum value of 'd' = S + X = 32.21 + 9 =41.21 m (b)    Distance between the two cars at the time ofapplying brakes = S = 32.21 m

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