Friends, this is a numerical homework problem. I tried my best to solve it but my answer is not matching with the one given at the back of the text book. Please help me out: A motor car moving at a speed of 72 km/h can come to a stop in 3 seconds, while a truck can come to a stop in 5 seconds. On a highway, the car is positioned behind the truck, both moving at 72 km/h. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it doesn't collide with the truck. The typical human response time is 0.5 sec.

My logic and answer: since car can decelerate to a stop much faster than the truck, it only need to worry about human response time which is 0.5sec. car would cover 10m in 0.5seconds at a speed of 72 km/h. so it just need to be 10m behind the truck minimum.

but the answer in the book is 1.25 m

How is this possible?


closed as off-topic by John Rennie, Abhimanyu Pallavi Sudhir, jinawee, Dilaton, David Z Feb 14 '14 at 16:25

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  • $\begingroup$ Your solution seems perfectly fine $\endgroup$ – Sandeep Thilakan Feb 14 '14 at 5:48
  • $\begingroup$ I'm not so sure. While the distance you calculated works, there's no guarantee that it's the minimum. $\endgroup$ – Javier Feb 14 '14 at 13:17
  • 1
    $\begingroup$ Try to draw the distance traveled of both as a function of time. And a quick note about your method, you also have to consider that the truck has not come to a stop after half a second, so it would also have moved forward a certain distance. PS : 1.25 meters does seems small. (I did got a larger answer). $\endgroup$ – fibonatic Feb 14 '14 at 13:50

You are missing the fact that the truck is still moving forwards during its decelleration interval.

  • $\begingroup$ That sounds like a vital clue! I will think over it $\endgroup$ – KawaiKx Feb 15 '14 at 14:59

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