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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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