Why Is The Speed, In General, Greater Than The Magnitude Of The Velocity?

From the definitions, we know that

\(Speed = \frac{Distance\;travelled}{Time\;taken}\)

And

\(Velocity = \frac{Displacement\;of\;body}{Time\;taken}\)

Consider the figure given below:

Why is the speed, in general, greater than the magnitude of the velocity?

From the figure, speed and velocity can be given as:

\(Speed = \frac{AB+BC}{t}\)

And

\(Velocity = \frac{AC}{t}\)

Substituting the values, we get

\(Speed = \frac{x+2y}{t}\)

And

\(Velocity = \frac{x}{t}\)

Therefore, speed is greater than speed.

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