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# Need help with math?

A van driver wants to pull out from rest onto a road where cars are moving at a constant speed of 20m/s. When there is a large enough gap between cars, the van driver pulls out immediately after one car passes. She then accelerates at a constant rate of 4m/s² until moving at 20m/s. To do this safely the car behind her must always be at least 10m away. Find the minimum length of the gap between the cars for the van driver to pull out

### 1 Answer

- RealProLv 76 months agoFavorite Answer
Let van driver start from x=0

When she reaches the speed of 20 m/s, she will be at x = (v^2 - (v0)^2) / (2a) = 50 m

Since her average speed in that period will be only half of 20 m/s, then the car in front of her will have covered twice as much so it will be at x=100 m

The car behind her needs to be at most x=40 m so minimum gap is 60 m.

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