Question

If a body travels in a circular track of radius 28m. after 3.5 revolution . find distance travel by a body, displacement travel by body, speed and velocity if 3.5 revolution in 50 second.

Answer 1

Answer:

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Explanation:

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Answer 2

Answer

• Distance = 616 m
• Displacement = 56 m
• Speed in 50 s = 12.32 m/s
• Velocity in 50 s = 1.12 m/s

Given

• A body travels in a circular track of radius 28 m and completes 3.5 revolutions

To Find

• Distance
• Displacement
• Speed in 50 s
• Velocity in 50 s

Concept Used

• 1 round of circular track = 2πr units
• Distance
• It is defined as how much ground occupied by an object
• Displacement
• It is defined as how far out of place an object is or shortest distance b/w two points i.e., initial and final points .
• Speed
• It is defined as total distance travelled per unit time

$\bf{\bigstar \;\; Speed=\dfrac{Distance}{Time}}\\\\\bf{\bigstar \;\; S=\dfrac{D}{t}}$

• Velocity
• It is defined as total displacement per unit time .

$\bf{\bigstar \;\; Velocity=\dfrac{Displacement}{Time}}\\\\\bf{\bigstar \;\; V=\dfrac{d}{t}}$

Solution

Case - 1 : Distance ( D )

Distance for 3.5 rounds of circular track :

⇒ 3.5 × ( 2π(28) )

⇒ 3.5 × ( 44 × 4 )

⇒ 3.5 × 176

⇒ 616 m

So , Distance , D = 616 m

Case - 2 : Displacement ( d )

Displacement for 3.5 rounds of circular track :

We know that displacement for 1 complete round of circular track is " 0 " .

Since , Initial and final points are same .

So , for 3 complete rounds displacement is " 0 ".

So , we need to find displacement for remaining half round .

For half round of circular track , displacement is equals to diameter of

circle . So ,

Displacement , d = 2 × r

⇒ d = 2 × 28

⇒ d = 56 m

So , Displacement , d = 56 m

Case - 3 : Speed in 50 s

Distance , D = 616 m

Time , t = 50 s

Apply formula for speed .

$\implies \rm Speed=\dfrac{Distance}{Time}\\\\\implies \rm S=\dfrac{D}{t}\\\\\implies \rm S=\dfrac{616}{50}\\\\\implies \rm S=12.32\ m/s$

Case - 4 : Velocity in 50 s

Displacement , d = 56 m

Time , t = 50 s

Apply formula for velocity .

$\implies \rm Velocity=\dfrac{Displacement}{Time}\\\\\implies \rm V=\dfrac{d}{t}\\\\\implies \rm V=\dfrac{56}{50}\\\\\implies \rm V=1.12\ m/s$

More Info

$\boxed{\begin{minipage}{4.5cm} \underbrace{\bf{\red{Equations\ of\ motion}}}\ :\\\\\rm \bigstar \;\; v=u+at \\\\\rm \bigstar \;\; s=ut+\dfrac{1}{2}at^2\\\\\rm \bigstar \;\; v^2-u^2=2as\\\\\rm \bigstar \;\; S_n=u+\dfrac{a}{2}[2n-1] \end{minipage}}$