Question

The kinetic energy of an object of mass ‘m' moving with a velocity of 2.5 m/s is 25J. What will be it’s kinetic energy when its velocity is increased 3 times?
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Answer 1

BY DATA

Let the mass be m

Kinetic energy , k = 25 J

Velocity ,v = 2.5 m/ s

Kinetic energy, k = mv²/2

$25 = \dfrac{m \times (2.5)^2}{2} \\ \\ m = \dfrac{25/times2}{6.25} \\ \\ m = \frac{50}{6.25} \\ \\m = 8 \: kg$

The mass of the object, m is 8 kg.

BY SECOND DATA

Mass, m = 8 kg

Velocity is increased three times.

v = 3 × initial velocity

v = 3 × 2.5

v = 7.5 m/s

Final kinetic energy = (m × v²) /2

$k = \dfrac{8 \times (7.5)^2}{2} \\ \\ k = 4\times56.25 \\ \\ k=225\: joule$

The final kinetic energy when the velocity is increased by three times is 225 J.

Answer 2

K.E. = ½mv²

25 = ½m(2.5)²

m= 8kg

New K.E. = ½×8× (2.5×3)² =225 J

Or it can be done as if velocity increase by 3 times kinetic energy increase by 9 times.

So, new kinetic energy 25×9=225J