Question

calculate the decrease in kinetic energy of a moving body if its velocity reduces to half of the initial velocity

Answer 1

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Answer 2

Answer:  The decrease in the kinetic energy is $\frac{3}{8}mu^{2}$.

Explanation:

The formula to find the decrease in the kinetic energy is as follows;

$Change\ in\ K.E= \frac{1}{2}mv^{2}-\frac{1}{2}mu^{2}$

Here, u and v are the initial and the final velocities and m is the mass of the object.

It is given in the problem that the velocity of the moving body reduces to half of the initial velocity.

Calculate the decrease in the kinetic energy.

$Change\ in\ K.E= \frac{1}{2}mv^{2}-\frac{1}{2}mv^{2}$

Put $v=\frac{1}{2}u$

$Change\ in\ the \ kinetic\ energy=-\frac{1}{2}m(\frac{1}{2})v^{2}-\frac{1}{2}mu^{2}$

$Change in the kinetic energy=-\frac{3}{8}mu^{2}$

Therefore, the decrease in the kinetic energy is$\frac{3}{8}mu^{2}$.