A particle is fallingdown into a medium with an initial velocity of 30m/s. If the acceleration of the particle is =(−4t)/m/s^2 , where t is in seconds, determine the distance traveled before the particle stops.

The distance traveled by the particle before it stops is 41.06 m.

Explanation:

We can find the distance traveled by the particle using the following equation:

Where:

: is the final velocity = 0 (when it stops)

: is the initial velocity = 30 m/s

a: is the acceleration = -4t m/s²

t: is the time

d: is the distance

First, we need to calculate the time:

Now, the acceleration is:

Hence, the distance is:          

Therefore, the distance traveled by the particle before it stops is 41.06 m.

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