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Displacement is a vector quantity that refers to how far out of place an object is; it's the object's overall change in position. In physics, specifically kinematics, we define displacement as the shortest path between the starting point and the ending point of an object's journey. Unlike distance, displacement considers direction.

For instance, in the example where Harry walks from a position of \(x=-12\) m to \(x=-47\) m, we calculate displacement by subtracting his initial position \(x_i\) from his final position \(x_f\). So, displacement \(= x_f - x_i = (-47) - (-12) = -35 m\). Here, the negative value indicates that the displacement is 35 meters to the left. Not to be mistaken with distance which would be the magnitude of this value ignoring the direction.

Velocity is a fundamental concept in kinematics, denoting the speed of an object in a specific direction. The rate at which an object changes its position is called velocity and its standard unit of measurement in the International System of Units (SI) is meters per second (\(ms^{-1}\)).

To calculate velocity, you need to know both the displacement and the time taken. The equation for velocity is \(v = \frac{d}{t}\) where

• \(v\) is velocity,
• \(d\) is displacement, and
• \(t\) is the time taken.

Applying this to Harry's walk, with a displacement of -35 meters and time of 35 seconds, his velocity is found as \(v = \frac{-35 m}{35 s} = -1 ms^{-1}\). The negative sign reflects the direction of Harry's walk, indicating he moved towards the left.

Kinematic equations allow us to predict the motion of an object when its velocity is either constant or changing at a constant rate (acceleration). These equations tie together velocity, acceleration, displacement, initial velocity, and the time taken.

There are four key kinematic equations each with a specific use depending on the information available and what you are trying to find:

1. \(v = v_0 + at\) (Final velocity given initial velocity, acceleration, and time)
2. \(s = v_0t + \frac{1}{2}at^2\) (Displacement given initial velocity, acceleration, and time)
3. \(v^2 = v_0^2 + 2as\) (Final velocity given initial velocity, displacement, and acceleration)
4. \(s = vt - \frac{1}{2}at^2\) (Displacement given final velocity, acceleration, and time)

These equations serve as the foundation for solving many problems in kinematics where acceleration is constant. However, in Harry's case, since acceleration isn't mentioned and the context suggests constant velocity, these equations can provide deeper insight if additional variables are considered.