Quantities in Physics

Measurement:
Motion is the change in the position of a body (i.e a car) with respect to time. We have a standard of measurement so that they way of describing the change in position means the same thing to everyone.

Standard of Measures:
Nearly all quantities in the physical world, can be expressed in terms of four fundamental quantities.
The four fundamental quantities are those of length, time, mass, and electric current. All other quantities are called derived quantities, because their measurement involves the measurement of two or more of the fundamental quantities.
The standards we will use in this unit are length, time and mass.
A standard must be unchanging, accessible, and reproducible.
The relationship between a derived quantity and the fundamental quantities can be made clear by the use of dimensions. When using dimensions we represent length by L, mass by M and time by T.

Dimensions of Some Common Quantities:
Quantity: Area, Relationship: length x breadth, dimensions: L square (in number form)
Quantity: Velocity, Relationship: displacement over time, dimensions: L T to the power of minus 1.
Quantity: Acceleration, Relationship: velocity over time (meaning that we need to find the velocity of an object before finding the acceleration of it, that is, if you want to find it), dimensions: LT over the power of LT-2.
Quantity: Force, relationship: mass X acceleration, dimensions: M L T to the power of negative 2
Quantity: Momentum, relationship: mass X velocity, dimensions: M L T to the power of negative 1.
Quantity: Work, relationship: force X distance, dimensions M L square T to the power of negative minus one.

Scalar and Vector Quantities:
A scalar quantity has magnitude but no direction. Distance is an example of a scalar quantity. It is measured in meters but has no direction.
A vector quantity has magnitude and also direction. The vector quantity displacement is the measure of the distance between where an object started and where it finished for example, 100 m and since vector quantities includes direction also, 100 N.
A vector may be represented by a line with an arrowhead, where the 'scaled' length of the line represents the magnitude of the vector and the arrowhead shows the direction.
i.e: vectors will look like this...

---------------------->
   20km east.

Change in velocity = final velocity - initial (starting) velocity

Speed and Velocity: 


Speed:
average speed = distance/time taken
                      s = d/t

The term average speed is called that because even when an object is travelling on a straight road, there are minor changes in the objects speed due to the surface of the road as it might be bumpy etc.
Speed is usually measured in meters per second, m s over the power of one or m/s.

The formula again:
speed   = d/t
       av 
We need to distinguish between average and instantaneous speed.
The instantaneous speed of an object is the speed of the object at any given moment.

Velocity:
Velocity is a vector quantity, it has magnitude and direction.
Velocity is defined as the time rate of change in displacement (displacement meaning the magnitude and direction--so, the time rate of the change in direction and magnitude of an object i.e: a travelling car). This simply means that average velocity is the displacement divided by the time taken.

Average velocity = displacement / time taken.

In dimensions:
v    = s /t
 av
v   = average velocity, measured in meters per second.
 av
s = displacement, measured in meters
t = time, measured in seconds

When acceleration is constant:
average velocity = final velocity + initial velocity / 2

v    = v + u / 2
 av 

Acceleration:
Acceleration is the time rate of change in velocity. This means that we can find the acceleration of an object by dividing the change in its velocity by the change in time.

Acceleration = change in velocity / change in time.

a = v / t
a = v - u (final velocity - initial velocity) / t
This equation can also be written in the form: v = u + at


When calculation if the calculation has a negative sign in front of the answer it means that the person or object is slowing down, or decelerating.

Displacement:
Displacement is the distance moved by an object in a specified direction. Displacement is a vector quantity (it has both magnitude and direction).


The equation for displacement is:
s = ut + 1/2 at the the power of 2 (square)


                     2
s = ut + 1/2at


Where:
s = displacement measured in meters (m)
u = initial (starting) velocity measured in meters per second.
a = acceleration.
t = time measured in seconds (s)

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