16. (i) (a) if the kinetic energy of a particle is tripled, by what
factor has its speed increased? (b) if the speed of a particle
is halved, by what factor does its kinetic energy change?

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 =

(a) Since the kinetic energy is tripled then

New kinetic energy = 3 * old kinetic energy

On cancelling the common terms of both side, we get

Squaring on both sides ,we get

So the speed is increased by factor of square root when the kinetic energy is tripled.

(b) Similarly, if speed is halved, then

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.

the components of a vector are the parts of the vectors that are to each other.

b perpendicular