Question

Find the increase in kinetic energy of a body of mass 500 g ,when its speed
increases from 2 m/s to 4 m/s.​

Answer 1

Answer:

increase in kinetic energy = kinetic energy final - kinetic energy initial 3J

Explanation:

500g = 0.5kg

kinetic energy initial

$ke \: = \frac{1}{2} m {v}^{2} \\ = \frac{1}{2} \times 0.5 \times {2}^{2} \\ = 1j$

kinetic energy final

$ke = \frac{1}{2} m {v}^{2} \\ = \frac{1}{2} \times 0.5 \times {4}^{2} \\ = 4j$

4j - 1j

3joules

Answer 2

Answer :

• Increase in kinetic energy possessed by the body, ∆K.E. = 3 J.

Explanation :

Given :

• Mass of the body, m = 500 g or 0.5 kg
• Velocity of the body, v₁ = 2 m/s
• Velocity of the body, v₂ = 4 m/s

To find :

• Increase in kinetic energy possessed by the body, ∆K.E. = ?

Knowledge required :

• Formula for Kinetic energy possessed by a body :

⠀⠀⠀⠀⠀⠀⠀⠀⠀K.E. = ½mv²⠀

[Where, K.E.,m and v are the kinetic energy possessed by the body, mass of the body and velocity of the body, respectively.]

• Formula for change in kinetic energy possessed by a body :

⠀⠀⠀⠀⠀⠀⠀⠀⠀∆K.E. = K.E.₂ - K.E.₁⠀

[Where, ∆K.E., K.E.₂ and K.E.₁ are the change in kinetic energy possessed by the body, final kinetic energy possessed by the body and initial kinetic energy possessed by the body, respectively]

Solution :

To find the initial kinetic energy possessed by the body :

⠀By using the formula for Kinetic energy possessed by a body and substituting the values in it, we get :

⠀⠀=> K.E. = ½mv²

⠀⠀=> K.E.₁ = ½ × 0.5 × 2²

⠀⠀=> K.E.₁ = ½ × 0.5 × 4

⠀⠀=> K.E.₁ = 0.5 × 2

⠀⠀=> K.E.₁ = 1

⠀⠀⠀⠀⠀∴ K.E.₁ = 1 J

Hence the initial kinetic energy possessed by the body is 1 J.

To find the final kinetic energy possessed by the body :

⠀By using the formula for Kinetic energy possessed by a body and substituting the values in it, we get :

⠀⠀=> K.E. = ½mv²

⠀⠀=> K.E.₂ = ½ × 0.5 × 4²

⠀⠀=> K.E.₂ = ½ × 0.5 × 16

⠀⠀=> K.E.₂ = 0.5 × 8

⠀⠀=> K.E.₂ = 4

⠀⠀⠀⠀⠀∴ K.E.₂ = 4 J

Hence the final kinetic energy possessed by the body is 4 J.

To find the change in kinetic energy possessed by the body :

⠀By using the formula for change in Kinetic energy possessed by a body and substituting the values in it, we get :

⠀⠀=> ∆K.E. = K.E.₂ - K.E.₁

⠀⠀=> ∆K.E. = 4 - 1

⠀⠀=> ∆K.E. = 3

⠀⠀⠀⠀⠀∴ ∆K.E. = 3 J

Hence the change in kinetic energy possessed by the body is 3 J.