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