Question

How much work is done on 2kg object when it changes it's velocity from 20 m/s to 40 m/s?

Answer 1

${\huge{\boxed{\mathcal{\red{Answer}}}}}$

Work done = 1200J

${\huge{\boxed{\mathcal{\red{Explanation}}}}}$

Work is said to be done when force is applied on a body and the body undergoes displacement.

S.I unit of work is joule.

Now, according to law of conservation of energy.

The energy required to do the work is equal to the change in potential and kinetic energy of system.

Thus we can say that the work done is change in kinetic energy of system.

Now, Initial kinetic energy of object :

$= \frac{1}{2} \times m {v}^{2}$

(v) In this case is initial velocity of object.

$= \frac{1}{2} \times 2 \times {20}^{2}$

$= {20}^{2}$

$= 400j$

Now final kinetic energy of object :

$= \frac{1}{2} \times m {v}^{2}$

(v) in this case is final velocity of object.

$= \frac{1}{2} \times 2 \times {40}^{2}$

$= {40}^{2}$

$= 1600j$

Now change in kinetic energy = Final kinetic energy - Initial kinetic energy

$= 1600j - 400j$

$= 1200j$

Therefore the work done on body is 1200J.

______________________________________

BY√\________________ SCIVIBHANSHU

THANK YOU

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Answer 2

Change in kinetic energy:-

½mv² - ½mu² = ½m(v² - u²) = ½m(v + u)(v - u)

We have,

Mass = 2kg

Former velocity = 20 m/s

Final velocity = 40 m/s

∴ Work done = ½ × 2kg(40m/s + 20m/s)(40m/s - 20 m/s)

⇒W = 1 kg(60 m/s)(20 m/s)

⇒W = 1200 Nm

⇒W = 1200 J {Answer}