Question

A cyclist completes full round of a circular track of radius 318 m in 1.5 min, Find its speed and velocity? Plz answer this in steps, it would help me a lot

Answer 1

Given:

A cyclist completes full round of a circular track of radius 318 m in 1.5 min.

To find:

Speed and Velocity of cyclist.

Calculation:

Speed is defined as the total distance divided by the time taken to cover that distance.

$\rm{speed = \dfrac{distance}{time} }$

$= > \rm{speed = \dfrac{2\pi r}{t} }$

$= > \rm{speed = \dfrac{2\pi (318)}{1.5 \times 60} }$

$\boxed{ = > \rm{speed = 22.2 \: m {s}^{ - 1} }}$

Velocity is defined as the total Displacement divided by the time taken to cover the specific Displacement.

Here Displacement is zero , because the cyclist starts and stops at the same point.

$\rm{velocity = \dfrac{displacement}{time} }$

$= > \rm{velocity = \dfrac{0}{1.5 \times 60} }$

$\boxed{ = > \rm{velocity = 0 \: m {s}^{ - 1} }}$

Hope It Helps.

Answer 2

Question:-

A cyclist completes full round of a circular track of radius 318 m in 1.5 min, Find its speed and velocity?

Answer:-

We need to convert time from minutes to the SI unit i.e, seconds

1.5 min = 60s + 30s = 90s (time taken)

Speed:-

Speed = (Distance covered) / (Time taken)

and distance covered is equal to circumference

So, distance = 2πr = 2 * (22/7) * 318 = 1998 m

So, Speed = (1998m) / (90s)

=> Speed = 22.2 m/s

Velocity:-

Velocity = (Displacement) / (Time taken)

and displacement is the change in position vector of an object. In other words, it is the shortest path between two points. And displacement is a vector quantity (it has direction as well as magnitude and unit).

As the cyclist is moving in a circular path, and it completes a full round, we can say that it came back to the initial point from where it started. So, it's displacement is 0.

So, Velocity = (0m) / (90s)

=> Velocity = 0m/s

Ans. Speed = 22.2m/s and Velocity = 0m/s