Explain distance, displacement, speed, velocity and acceleration with a sporting example of each.

Concept understanding — Center Of Gravity Balance

The Intuition: The One Point That Holds Everything Together

Think about balancing a pencil on your finger. You slide it back and forth until you find that one spot where it stays perfectly horizontal. That spot isn't random — it's the point where the pencil's weight on the left exactly cancels the weight on the right. If you put your finger anywhere else, the pencil tips.

Now imagine a much more complicated object: a chair, a cricket bat, or even your own body. Every tiny piece of that object is pulled downward by gravity. The center of gravity is the single point where you could pretend all that weight is concentrated. If you support the object exactly at that point, it balances perfectly — no tipping, no rotation.

Note

For most objects on Earth, the center of gravity is the same as the center of mass. The distinction matters only when gravity varies significantly across the object (e.g., a very tall building), which you won't see in school-level problems.

The Precise Statement

The center of gravity of an object is the point at which the entire weight of the object can be considered to act, for the purpose of analyzing translational and rotational equilibrium under gravity.

Mathematically, for a system of particles with weights $w_1, w_2, \dots, w_n$ located at positions $(x_1, y_1, z_1), \dots, (x_n, y_n, z_n)$ , the coordinates of the center of gravity are:

x_{CG} = \frac{\sum w_i x_i}{\sum w_i}, \quad y_{CG} = \frac{\sum w_i y_i}{\sum w_i}, \quad z_{CG} = \frac{\sum w_i z_i}{\sum w_i}

Since weight $w_i = m_i g$ , and $g$ is constant, this simplifies to the center of mass formula:

x_{CM} = \frac{\sum m_i x_i}{\sum m_i}, \quad y_{CM} = \frac{\sum m_i y_i}{\sum m_i}, \quad z_{CM} = \frac{\sum m_i z_i}{\sum m_i}

\vec{R}_{CG} = \frac{\sum m_i \vec{r}_i}{\sum m_i}

Why It Matters …

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Distance (path length), displacement (straight-line change of position), speed (distance/time), velocity (displacement/time, with direction) and acceleration (rate of change of velocity) — each with a sporting example.

Distance — the total length of the path travelled, regardless of direction (a scalar). Example: a runner completing one lap of a 400 m track covers 400 m of distance.
Displacement — the straight-line distance from start to finish in a stated direction (a vector). Example: the same runner returning to the start line has a displacement of 0 m.
Speed — the rate of covering distance, speed = distance / time (a scalar). Example: a swimmer covering 50 m in 25 s has a speed of 2 m/s.
Velocity — the rate of change of displacement in a given direction, velocity = displacement / time (a vector). Example: a sprinter running 100 m north in 10 s has a velocity of 10 m/s north. …

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Q.Explain distance, displacement, speed, velocity and acceleration with a sporting example of each.

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