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Velocity is a key concept in kinematics as it describes how fast an object is moving in a specific direction. It is a vector quantity, which means it has both magnitude (speed) and direction. For example, when the Australian emu dashes north at a speed of \(13.0\ \mathrm{m/s}\), this entire description signifies **velocity** because it includes both how fast it is moving and its direction.
The velocity can change in two main ways:

• Change in Speed: The emu slows down from \(13.0\ \mathrm{m/s}\) to \(10.6\ \mathrm{m/s}\).
• Change in Direction: Velocity changes even if the speed remains constant but the direction alters, which isn't the case for the emu. It continually moves north.

Remember, if an object is moving in a straight path and its speed changes, the velocity changes accordingly. Understanding velocity is crucial for solving problems about motion, such as calculating eventual speeds or predicting future positions of moving objects.

Acceleration refers to the rate at which an object changes its velocity. Like velocity, acceleration is also a vector, having both magnitude and direction. In our example problem, the emu experiences a negative acceleration or deceleration as it reduces its speed. This indicates that the acceleration is directed opposite to the direction of motion, which in this case is south while the emu runs north.
The formula to calculate acceleration is given by:\[a = \frac{v_f - v_i}{t}\]Where:

• \(a\) = acceleration
• \(v_f\) = final velocity \(10.6\ \mathrm{m/s}\)
• \(v_i\) = initial velocity \(13.0\ \mathrm{m/s}\)
• \(t\) = time taken \(4.0\ \mathrm{s}\)

Using these, the emu's acceleration is calculated as \(-0.6\ \mathrm{m/s}^2\). This negative sign indicates the direction is opposite to the initial direction of motion. With this concept, you can also determine future velocities by applying this constant acceleration over a new time interval.

Motion describes the change in position of an object over time. In kinematics, motion can take many forms such as straight-line or curvilinear, and can vary between constant speed, acceleration, or deceleration. For our emu, the motion under analysis is in a straight line towards the north, demonstrating both initial speed and a slowing down process.
To determine the new velocity of our emu after an additional \(2.0\ \mathrm{s}\) of motion, we use the simple kinematic equation:\[v = v_i + a \cdot t\]Here, the previous velocity \(v_i = 10.6\ \mathrm{m/s}\), acceleration is \(-0.6\ \mathrm{m/s}^2\), and the time is \(2.0\ \mathrm{s}\). The calculated new velocity is \(9.4\ \mathrm{m/s}\), which means the emu continues its motion north but at a slower pace as it continues to decelerate. Understanding these principles is vital for predicting how objects move, calculate when they will stop, or determine the moment they could switch directions.