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You’re speeding at 85 km/h when you notice that you’re only 10

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You’re speeding at 85 km/h when you notice that you’re only 10 m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car negatively accelerates at 4.2 m/s 2 . Assuming the other car continues at constant speed, will you collide? If so, at what relative speed ? If not, what will be the distance between the cars at their closest approach?

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You’re speeding at 85 km/h when you notice that you’re only 10 m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car negatively accelerates at 4.2 m/s 2 . Assuming the other car continues at constant speed, will you collide? If so, at what relative speed ? If not, what will be the distance between the cars at their closest approach?

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Text solutionVerified

We know the following equation:

x = v_{0} t + \frac{1}{2} a t^{2}

Thus, we find:

x_{20} + v_{20} t = v_{10} t + \frac{1}{2} a t^{2}

0 = v_{10} t + \frac{1}{2} a t^{2} - x_{20} - v_{20} t

Solving for t by applying the quadratic formula, we plug in the known values to find:

t = \frac{( 23.61 - 16.67 ) \pm ( 23.61 - 16.67 ) ^{2} - 4 ( \frac{- 1}{2} ) ( 4.2 ) ( 10 )}{- 4.2 \times 2 \times \frac{1}{2}} = 1.085 seco n d s

Thus, we find the velocity of the second car:

v = v_{1} - 60 km / h

v = (23.61 - (4.2) (1.085)) (3.6 \frac{km / h}{m / s}) - 60 km / h = 8.59 km / h

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Question Text	You’re speeding at 85 km/h when you notice that you’re only 10 m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car negatively accelerates at 4.2 m/s 2 . Assuming the other car continues at constant speed, will you collide? If so, at what relative speed ? If not, what will be the distance between the cars at their closest approach?
Topic	All topics
Subject	Physics
Class	Class 11
Answer Type	Text solution:1

Text solutionVerified

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