Kinematics Numerical 1(Cyclist, speed and velocity)
Kinematics Numerical 1: A cyclist completes half round of a circular track of radius 318 m in 1.5 minutes. Find its speed and velocity.
Solution:
We have been given the following data;
Radius=r= 318 m
Time=t=1.5 min
Speed=v=?
Velocity=V=?
We first find speed
It is clear from the statement of the problem that track is circular and the cyclist covers a distance by tracking half circle.
We know that;
\[ Circumeference Of The Circle = 2\pi r \]
So;
\[ DistanceCoveredBy Cyclist=\frac{2\pi r}{2}=\pi r \]
So we have;
\[ Distance = S=\pi r=3.14\times 318=999m \]
We know;
\[ Speed=v=\frac{S}{t} \]
So,
\[ v=\frac{999}{90}=11.1\frac{m}{sec} \]
Now we find Velocity;
We know the cyclist by traveling a distance finally reaches from point A to point B. A straight line from initial position to final position represents ‘displacement’ – So, in this case , displacement of the cyclist is equal to ‘2r’ – as is clear from fig above.
so,
Displacement=d=2r=2×318=636 m
We know;
\[ Velocity=\frac{Displacement}{Time} \]
or
\[ V=\frac{d}{t} \]
So,
\[ V=\frac{636}{90}=7.07\frac{m}{sec} \]
Copyright secured by Digiprove © 2020