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A particle moves over three quarters of a circle of radius $r$ in time $t$. What is the velocity of the particle?
As given, a particle moves over three quarters of a circle of radius $r$.
The motion of the particle has been shown in the diagram below:
$AB$ is the displacement,
To find $AB$, let us use Pythagoras theorem in $\vartriangle AOB$
$AB^2=OA^2+OB^2$
Or $AB^2=r^2+r^2$
Or $AB^2=2r^2$
Or $AB=\sqrt{2r^2}$
Or $AB=r\sqrt{2}$
Now, the velocity of the particle $=\frac{displacement}{time}$
$=\frac{r\sqrt{2}}{t}$
Updated on: 10-Oct-2022
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