# Velocity as a property

Is velocity considered to be a property like mass and weight that can be measured at a single moment in time, such as mass of X measured at time T1, or is it a property that needs to be measured over a period of time because it implies change?

• Weight is not a property of an object although mass is, a rock of 5 kg does not have same weight on the moon as it does on Earth. Velocity Is not a property either, as an objects velocity will change as the forces on it change. If you think a little about the process behind say, throwing an object upwards into the air, this might help – StudyStudy Jan 19 at 23:53
• @StudyStudy An objects velocity will change as the forces on it change. Velocity changes even under a constant force. – G. Smith Jan 19 at 23:59
• Do you know calculus? For one-dimensional motion, velocity is defined as v = dx/dt. So you have to know how position changes with time for small time intervals about the point where you want to know the velocity. So yes, it implies change. – Not_Einstein Jan 20 at 0:04
• You should also check the difference between.speed and velocity, as I should do myself..... – StudyStudy Jan 20 at 0:06
• Velocity even changes with the reference frame that it is measured in. – Bob D Jan 20 at 0:41

Average velocity is the total change in displacement divided by the time taken. It can only be defined over a time interval, so takes a finite interval to measure. E.g. if a ball travels $$(3 \mathbf i + 2 \mathbf j)m$$ in 2s, its average velocity is $$(1.5 \mathbf i + \mathbf j)ms^{-1}$$.

Instantaneous velocity is the derivative of displacement with respect to time, so is the limit of the average velocity as the time taken goes to zero. E.g. if the displacement is given by $$\mathbf x (t) = \frac{1}{2} \mathbf a t^2$$ then the velocity is $$\mathbf v (t) = \mathbf a t$$. It is defined at every point in time, and theoretically requires no time interval to measure (although it would obviously take time to measure it this is related to the use of measuring instruments, not the definition of velocity)

How do you measure mass at a single moment in time?

You can put a mass on a spring scale and see how far the spring stretches, and compare that against known masses.

You can apply a known force to it and see how fast it moves.

However, mass is considered to be intrinsic to -- to things that have mass.

Velocity is only velocity relative to something else. Velocity in an arbitrary frame.

You measure mass relative to other masses too. Like, hit a mass with a BB from a BB gun, and measure how much they each change velocity. You compare to a known mass.

Somehow mass seems less arbitrary to me, though. With velocity you can arbitrarily decide what zero velocity is, to fit your convenience. You can't just decide that something has zero mass to make your calculations simpler. If it has mass, then it really does have mass itself.

• Thank you all for your replies and comments. Very useful and they answered my question. – Miles Esfahani Jan 22 at 0:10