#### 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?

**SOLUTION:**

Part a

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

Part b

We have the same given values from part a. So we have

Part c

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

Part d

We have the same given values.

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