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Derivatives are rates of change, and in the physical world that means things like velocity and acceleration. In fact, studying these quantities played a major role in the invention of Calculus.

A ball is currently \( 1000m \) above the ground and held at rest. It is dropped at \( t = 0 \), and experiences gravitational acceleration of \( 9.8 \, m / s^2 \).

When \(3\) seconds is passed, what is the height of the ball from the ground?

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**P** with an initial velocity of \(9\text{ m/s}\) starts to move eastward along a straight line under a constant acceleration of \(8\text{ m/s}^2\) from point **A**. At the same time, another object **Q** starts to move eastward under a constant acceleration of \(9\text{ m/s}^2\) from rest at point **A**. How far does object **Q** travel in meters when the two objects meet again?

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The speed of a bullet is measured to be \( 640 \text{ m/s} \) as the bullet emerges from its \( 1.20 \text{ m} \) long barrel. Assuming a constant acceleration, find the time that the bullet spends in the barrel after it is fired.

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