Question

Question:-

1. Explain kinetic energy.
2. Derive the formula of kinetic energy.

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Answer 1

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• Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion
• Kinetic energy can never be negative and it is a scalar quantity
• i.e. it provides only the magnitude and not the direction

K.E. = 1/2 m v2.

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Answer 2

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1. Kinetic energy

⟶ The energy of a body due to its motion is called kinetic energy.

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• Examples of kinetic energy:-

⟶ A moving cricket ball

⟶ Running water

⟶ A moving bullet

⟶ Flowing wind

⟶ A moving car

⟶ A running athlete

⟶A rolling Stone

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⟶ Kinetic energy is directly proportional to mass and the square of velocity.

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2. Formula of kinetic energy

⟶ If an object of mass 'm' moving with uniform velocity 'u', it is displacement through a distance 's'. Constant force 'f' acts on it velocity changes from 'u' to 'v'.

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⟶ Then acceleration is 'a'.

$\sf \: W=F×S - - - - - (i)$

$\sf \: F=ma - - - - - (ii)$

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⟶ According to third equation of motion, relationship between u, v, s and a is as follows

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$\sf {v}^{2} - {u}^{2} = 2as$

$\implies \sf \: S = \frac{ {v}^{2} - {u}^{2} }{2a} \: - - - - (iii)$

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Now, Putting the value of f and S from (ii) and (iii) in equation (i)

$\sf \: W = ma \times \frac{ {v}^{2} - {u}^{2} }{2a}$

$\sf \longrightarrow \: \frac{m}{2} \times {v}^{2} - {u}^{2}$

$\sf \longrightarrow \: \frac{1}{2} m( {v}^{2} - {u}^{2} )$

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If u = 0

$\sf \: W = \frac{1}{2} m {v}^{2}$

$\sf \: ∴E_k= \frac{1}{2}m {v}^{2}$

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