A train starts from rest and accelerates uniformly with a = 2 m/s2 until it has...

A train starts from rest and accelerates uniformly with a = 2 m/s² until it has traveled 1 km. The train then moves at a constant velocity of 20 m/s for one hour. The train then slows down uniformly at 0.05 m/s², until it stops. Calculate:

The maximum speed of the train
The total distance traveled by train.

Expert Solution

In the first part, the train accelerates uniformly starting from rest and reaches to the final velocity of 20 m/s. In this process velocity increases from zero to this final velocity.
Then it moves at this constant velocity of 20 m/s for one hour. In this process the velocity remains unchanged.
In the last part of the journey, the train slows down uniformly. So, its velocity decreases. Thus we see that the maximum velocity is

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In the first the distance travelled is given and is

In the second part, the distance travelled is computed as

In the last part the distance travelled is computed as

So, the total distance is

genius_generous answered 2 years ago

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