Question

a body completes one revolution in a circular path of radius 20m in 4s. find the average velocity and speed after half revolution

Answer 1

Given :-

A body completes one revolution in a circular path of radius 20 meters in 4 seconds

Required to find :-

• Average velocity & speed after traveling half of the revolution

Formula used :-

$\tt{\bf{ Speed = \dfrac{ Distance}{ Time } }}$

$\tt{\bf{ Average \; velocity = \dfrac{ Total \; displacement }{ Total \; time \; taken } }}$

Solution :-

Given that :-

A body completes one revolution in a circular path of radius 20 meters in 4 seconds

we need to find the average velocity & speed after half revolution .

So,

In order to find the speed after half revolution .

First , we need to find the distance travelled in one revolution .

Here,

The distance travelled in one revolution is equal to the perimeter/circumference of the circle .

Now,

Let's find the circumference of the circle

Radius = 20 meters

Using the formula ;

Perimeter of the circle = 2π r

Perimeter of the circle = 2 x 3.14 x 20

Perimeter of the circle = 125.6 meters

This implies ;

The distance travelled in one revolution = 125.6 meters

Now, let's find the speed of the body throughout the whole journey ;

Here,

Distance = 125.6 meters

Time = 4 seconds

Using the formula ;

$\tt{\bf{ Speed = \dfrac{ Distance}{ Time } }}$

speed = 125.6/4

speed = 31.4 m/s

Similarly,

Now let's find the time taken by the body to travel half revolution ;

Speed = 31.3 m/s

Distance = 125.6/2 = 62.8 meters

Time = ?

=> Time = Distance/ Speed

=> Time = 62.8/31.3

=> Time = 2 seconds

So,

Time taken to travel half of the revolution is 2 seconds .

This states the fact that the object posses an uniform circular motion .

This implies ;

• Speed of the body when travelled half revolution = 31.3 m/s

Now,

Let's find the Average velocity ;

Total displacement is equal to the diameter of the circle

Because, the diameter is the shortest path between them

So,

Length of the diameter = Total displacement

Length of the diameter = 2 x radius

Length of the diameter = 2 x 20

Length of the diameter = 40 meters

So,

• Total displacement = 40 meters

Time taken = 2 seconds

Using the formula ;

$\tt{\bf{ Average \; velocity = \dfrac{ Total \; displacement }{ Total \; time \; taken } }}$

Average velocity = 40/2

Average velocity = 20 m/s

Hence,

• Average velocity = 20 m/s