The driver of a brand new Porsche is recklessly speeding down the highway and pl

Question

The driver of a brand new Porsche is recklessly speeding down the highway and playing with his cell phone. The digital speedometer gives a reading of 112.5 mph. When he glances back at the road he realizes that a Honda is only 100 m in front of his and is travelling at a mere 45 mph. Luckily for the driver of the Porsche, it has INSTA-TECT sensors in front and is able to slam on the brakes immediately. What magnitude acceleration does the Porsche need to barely avoid a collision with the Honda? Express your answer in SI units

a) Draw a complete pictorial representation of the situation.

b) Draw a position vs. time graph for both cars on the same graph.

c) Draw a velocity vs. time graph for both cars on the same graph.

d) Show your work and box your answer to the question.

Hint: What does "barely avoid" mean, mathematically?

Explanation / Answer

barely avoid means it will just touch honda.this is limit of acceleration if de-accelartion is just less than given then it will hit honda/.

relative velocity = 112.5 - 45 = 67.5 mph = 67.5 x 1609/3600 = 30.17 m/s

d= 100m

relative final velocity shud be zero.

using v^2- u^2 = 2ad

0 - 30.17^2= 3x 100x a

a = - 3.03 m/s2

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