# Two trains one travelling at 20m/s and the other 40m/s are headed toward one another along a straight level track. When they are 105 meters apart, each engineer sees the other's train and applies...

Two trains one travelling at 20m/s and the other 40m/s are headed toward one another along a straight level track. When they are 105 meters apart, each engineer sees the other's train and applies the brakes. The brakes decelerate each train at a constant rate of 10 m/s^2. Will the two trains collide? Explain quantitatively.

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### 1 Answer

The two trains headed toward each other along a straight level track are moving at 20 m/s and 40 m/s respectively. When they are 105 m apart the engineer in each of the trains sees the other and applies the brakes that result in a deceleration of 10 m/s^2.

Use the formula v^2 - u^2 = 2*a*s to determine the distance traveled by each of the trains before they come to a stop.

For the train traveling at 20 m/s, s = 20^2/(2*10) = 20 m and for the train traveling at 40 m/s, s = 40^2/(2*10) = 80. Adding the two gives 100 m. When the trains come to a stop they are 5 m apart.

**The two trains do not collide.**