If the velocity of an object quadruples while falling, by what factor would the kinetic energy and momentum increase, respectively?

Multiple Choice:

a) 4x and 4x

b) 4x and 2x

c) 16x and 4x

d) 16x and 16x

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The correct answer here is C -- the kinetic energy increases by a factor of 16 while the momentum only increases by a factor of 4.

The formula for kinetic energy is

k = 1/2mv^2 or k = .5*m*v*v

where m = mass and v = velocity.

Since the mass of the object remains constant as it falls, only the velocity changes on the right side of this equation. When the velocity goes up by 4 times, the kinetic energy goes up by 16 times because the velocity gets squared.

The formula for momentum is

momentum = mass*velocity

Here, velocity is not squared so multiplying the velocity by 4 only increases the momentum by a factor of 4.

Let the initial velocity of the object be v. At this velocity its kinetic energy, k1 is given by: k1 =**(1/2) mv^2**, where m is the mass of the object .

It's momentumP1 is given by ;P1 = **mv.**

Velocity when quadruple is 4v.

The kinetic energy k2 of the object at 4v velocity: k2 =(1/2)m(4v)^2 = **(16/2)mv^2**

The momentum P2 of the body at 4v velocity : P2 = m*(4v) **=4mv**

Therefore, by the above results we conclude that (c) is the correct choice.

Momentum is the total motion possessed by a body. Mathematically momentum can be represented by the formula:

Momentum = Mass*Velocity

This means that the momentum is directly proportional to the speed or velocity. Thus if the speed of an object is increased n times, its momentum will also be increased n times.

Kinetic energy of an objects refers to the energy that it possesses because of its motion, or velocity. This kinetic energy can be calculated by the formula:

Kinetic energy = (mass*Velocity^2)/2

This means that the kinetic energy is directly proportional to the square of speed or velocity. Thus if the speed of an object is increased n times, its kinetic energy will be increased n^2 times.

In the question given above the velocity of the object is increase 4 times. Therefore its momentum will also increase 4 times, and its kinetic energy will increase 4^2 times - that is 16 times.

Therefore option c) of the multiple choice is correct.

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