Question

a body of mass 10kg is acted on by a constant force of 20N for 3 seconds. calculate the kinectic energy at the end of the time

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Answer 1

Solution :

The mass of the body is 10 kg.

Force acting on the body : 20N

Force = Mass * Acceleration

> 20 = 10 a

> a = 2 m/s² .

According to the second law of motion :

s = ut + 1/2 at^2 .

u = 0

> s = 1/2 a t^2 .

> s = 1/2 * 2 * 9

> s = 9m .

Thus, the body travels a distance of 9m .

Kinetic energy is here equal to the work done by the body.

Work done = Force * Displacement

> 20N x 9m

> 180 Joules .

This is the required answer.

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Answer 2

Gɪᴠᴇɴ :

• Mass of a body is 10 kg.

$:\longrightarrow\:\:\bf{Mass\:(m)\:=\:10\:kg}$

• A constant force acts on it, i.e. 20 N, for 3 seconds.

$:\longrightarrow\:\:\bf{Force\:(F)\:=\:20\:N}$

$:\longrightarrow\:\:\bf{Time\:(t)\:=\:3\:s}$

Tᴏ Fɪɴᴅ :

• The kinetic energy at the end of the time.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

☆ First we calculate the acceleration of the body.

↝ Using Newton's second law,

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{Force\:=\:mass\times{acceleration}\:}}}}}}$

➛ $\sf{20\:=\:10\times{a}\:}$

➛ $\sf{a\:=\:\dfrac{20}{10}\:}$

➛ $\bf{a\:=\:2\:m/s^2}$

☆ Now, we calculate how much distance the should acquire, after force acted on it.

↝ Using equation of motion as,

$\pink\bigstar\:\:{\underline{\green{\boxed{\bf{\purple{S\:=\:u\:t\:+\:\dfrac{1}{2}\:a\:t^2\:}}}}}}$

Wʜᴇʀᴇ,

• S is the distance acquired by the body.

• u is the initial velocity of the body, i.e. 0 m/s, because body is at rest before force act's on it.

• t is the time period, i.e. 3 seconds.

• a is the acceleration of the body, i.e. 2 m/s².

➾ $\sf{S\:=\:0\times{3}\:+\:\dfrac{1}{2}\times{2}\times{3^2}\:}$

➾ $\sf{S\:=\:0\:+\:9\:}$

➾ $\bf{S\:=\:9\:m}$

Nᴏᴡ,

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\orange\bigstar\:\:{\underline{\pink{\boxed{\bf{\blue{Work\:done\:=\:Change\:in\:kinetic\:energy\:}}}}}}$

⇒ $\sf{kinetic\:energy\:=\:Work\:done}$

⇒ $\sf{kinetic\:energy\:=\:Force\times{Displacement}}$

⇒ $\sf{kinetic\:energy\:=\:20\times{9}}$

⇒ $\bf\pink{kinetic\:energy\:=\:180\:Joules}$

$\Large\bf{Therefore,}$

The kinetic energy at the end of the time is 180 J.