An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of as it goes through. The station is 210 m long.
(a) How long is the nose of the train in the station?
(b) How fast is it going when the nose leaves the station?
(c) If the train is 130 m long, when does the end of the train leave the station?
(d) What is the velocity of the end of the train as it leaves?
We are given
We are required to solve for time, t. So we have
If we rearrange the terms into a general quadratic equation, we have
Solve for t using the quadratic formula. We are given
Discard t=283.46 s as it can be seen from the problem that this is not a feasible solution. So, we have
We have the same given values from part a. So we have
We are given the same values as in the previous parts, except that for the value of x since we should incorporate the length of the train. For the distance, x, we have
Therefore, we have
You can solve this problem by the method presented in part a. But we can also rearrange the equation to solve for t, using also quadratic equation. We have
We have the same given values.
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