Is it possible to multiply two units together?If so, what would be the meaning of squaring velocity?

Answer 1

15 mph * 10 mph = 150 mph, not 150 mph^2

If you multiply Newtons (a unit of Force), and a distance like:

15 N * 10 meters, will equal to 150 N-m (Newton-meters), which is a pressure unit.

Answer 2

This is a truly insightful question. You clearly understand that paying attention to the units that go along with the values is important.

When multiplying two numbers with identical units, the units square as well (unlike what one answerer told you). But if the math you did has meaning in the real world (e.g., some physical meaning) the units can be broken out to make sense.

For example, in 1/2 M v^2, the units would in fact be kg (m/sec)^2. But we can break that out as kg (m/sec^2) m; where (m/sec^2) = a = acceleration, so we have kg a m and kg a is force (as in F = Ma) and m is the distance unit (e.g., meter). Force over a distance is defined as work and energy is the capability to do work. Thus 1/2 M v^2 is in the units of work (or energy), and that's a good thing because we all know 1/2 M v^2 is the equation for kinetic energy.

Answer 3

A good question, but let's get one thing clear.
We start with the mathematical statement of a real physical problem, and then proceed to solve it using known and established rules of physics and mathematics.

For example, if you refer your physics textbook for the derivation of the equations of motion, you will see that the equations are basically derived from two fundamental physics concepts, viz. a = (v - u)/t, and s = (u + v)t/2. One says acceleration is the rate of change of velocity, and the other that the displacement equals the average velocity multiplied by the time. When we eliminate time t between these two basic mathematical statements, we arrive at the equation v2 = u2 + 2as. v2 and u2 are squares of velocities. The terms v2 and u2 need not have any physical interpretation of their own. IT'S JUST THE WAY THE MATHEMATICS WORKS OUT.

As an exercise, go back to your textbook, and see how the derivation of the formula for kinetic energy evolves from the initial statement of the work-energy theorem. Again, the final formula 1/2 mv2 is just the way the maths works out.

Remember one thing. You must see the formula AS A WHOLE. The individual parts need not have a separate physical significance.

Once again, good question. It shows you have an active mind.

Answer 4

If we multiply or divide two quantities, the units for the result is also a multiplication or division of the original units:

20 Km / 2 hr = 10 Km/hr

2 ft x 2 ft = 4 ft^2

Squaring velocity - I take this to mean units like m^2/sec^2, a result of multiplying velocity be velocity. As a unit, it appears to have no physical meaning. But it can be equivalent to, for example, "energy / mass", so will be the "dimensions" for energy per unit mass.

Answer 5

You're not the first person to stumble on this. Sir Issac Newton thought momentum which is proportional to Velocity was the key. It was only in the 1800s did scientist realize the importance of Kinetic Energy (i.e. V squared). I think Dr. D's approach is the easiest to grasp the concept. Energy has to do with fields such as gravity and the change to matter (i.e., the amount velocity changes) as it changes position in those fields. >>>>>>>>>> Edit >>>>> This question has resulted in some very interesting posts. Since I posted my original answer, I really like Scythian's and Remember's posts from a philosophical perspective. (The remaining posts are all correct, but take a mathematical approach) Scythian ties into relativity which is that kinetic energy, only at low velocities, is proportional to v^2. After that you have to go to the famous E=MC^2 formula where M is the relativistic mass. Remember does a nice exploration of conservative fields, which is why energy is conserved either at relativistic or non-relativistic speeds.

Answer 6

Kinetic energy is 1/2 * M * V^2, so that it kind of like squaring velocity if the mass is assumed to be 1, or at least constant. But there is no useful physical interpretation of squaring the velocity only, as far as I know. It would simply be velocity squared.

Answer 7

Laws of physics do not change as per our need. They remain the same. The units always get multiplied and divided. This is correctly explained by "eyeonthe.." above. mtr^2/sec^2 is nothing but the unit of work done or energy.

We can have unit for a physical phenomenon. But we can not find a physical equivalent for every combination or multiplication of units.

Answer 8

Yes it is possible and there are many examples.
Length - meter Area - m^2 Volume m^3
Power - 1 watt = 1 Volt Ampere = 1 Newton meter per second
Force - 1 Newton = 1 kg m per second squared.
Pressure - 1 Pascal = 1 Newton per meter squared
Etc.

For squaring velocities m^2 per second squared I don't see a simple application.