Aman runs at a velocity of 4.5 m/s for 15.0 min. when going up an increasingly steep hill, he slows down at a constant rate of 0.05 m/s^2 for 90.0s and comes to a stop.
how far did he run?

The man ran  4252.5 meters.

Why?

To solve the problem, we need to divide the exercise into two movements, the first on while the was running at 4.5 m/s for 15 min, and then, while he was slowing down (going up because of the hill).

First movement: Running at 4.5 m/s for 15 min.

We need convert from minutes to seconds,

Now, calculating the distance covered for the first movement, we have:

So, we know that the man covered 4050m for the first movement, it will be our initial position for the second movement.

Second movement:  acceleration -0.05m/s^2 (because he's slowing down) for 90 seconds, at 4.5m/s.

Hence, we have that he ran 4252.5 m.

Have a nice day!

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