How Long Does Tara Have Before She Crashes?

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Tara is driving at 27 m/s in fog with a visibility limit of 30m, while a car ahead is moving at 10 m/s. When she sees the car, it is effectively 30m away. To calculate the time before a potential crash, consider the relative speed difference between the two vehicles, which is 17 m/s (27 m/s - 10 m/s). Tara will close the 30m gap in approximately 1.76 seconds, indicating she has just under 2 seconds before a collision occurs if she does not brake. Understanding the relative speeds and distances allows for a straightforward calculation of the time until impact.
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Tara is driving at 27 m/s through a fog that limits her visibility to 30m. She suddenly sees a car in front of her traveling in the same direction at 10 m/s. if she fails to apply the brakes, how much time does she have between seeing the car and crashing into it?


how do you do this question?
 
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You know her speed, and you know the distance between the two vehicles when she sees it. You also know the speed of the vehicle ahead. You have everything that you need. What do you need to derive to determine the elapsed time?
 
Since the second car only could have be seen 30m ahead he is starting 30m, and Tara starts with 0. Then after the first second Tara is at 27m and the second car is at 40m. At the 2nd second the second car is at 50m and Tara is at 54m, meaning she would have crashed at about 2 seconds
 
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Think. Is there another way to simplify this problem without calculating the actual positions of the vehicles at each unit of time?
 
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