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## Displacement, Velocity, Acceleration

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.

# Uniform Acceleration

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?

Object 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?

An object with an initial velocity of $$9\text{ m/s}$$ moves along the $$x$$-axis with constant acceleration. After $$8$$ seconds, its velocity is $$49\text{ m/s}.$$ How far did it travel during the $$8$$ seconds in meters?

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.

A car that is initially traveling at $$20\text{ m/s}$$ accelerates uniformly in a straight line for $$5$$ seconds at a rate of $$6\text{ m/s}^2.$$ How far in meters does the car travel during the $$5$$ second period?

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