The (a) speed increases by square root of 3 on tripling of kinetic energy and (b) kinetic energy is reduced by 1/4th if the speed is halved.
Explanation:
Kinetic energy is the energy exhibited or released by any body in motion. So kinetic energy is directly proportional to the product of mass and square of velocity.
K.E = [tex]\frac{1}{2}mv^{2}[/tex]
(a) Since the kinetic energy is tripled then
New kinetic energy = 3 * old kinetic energy
[tex]\frac{1}{2}mv_{new} ^{2} = 3 *\frac{1}{2}mv_{old} ^{2}[/tex]
On cancelling the common terms of both side, we get
[tex]v_{new} ^{2} = 3 v_{old} ^{2}[/tex]
Squaring on both sides ,we get
[tex]v_{new}=\sqrt{3} v_{old}[/tex]
So the speed is increased by factor of square root when the kinetic energy is tripled.
(b) Similarly, if speed is halved, then
[tex]kinetic energy = \frac{1}{2}m(\frac{v}{2})^{2}[/tex]
Kinetic energy = 1/4×old kinetic energy.
So if the speed is halved, then the kinetic energy will be reduced by 1/4 of old kinetic energy.
Thus, the (a) speed increases by square root of 3 on tripling of kinetic energy and (b) kinetic energy is reduced by 1/4th if the speed is halved.
