# Motion in One and Two Dimensions

## Motion in One and Two Dimensions

AOS 1 (40%): Motion in One and Two Dimensions
Explain motion in terms of Newton’s model & assumptions including;
Graphical description of motion: displacement-, velocity-, & acceleration-, time graphs.
For displacement-time (x-t) graphs; velocity (v) = gradient
For velocity-time (v-t) graphs; displacement (x) = area, acceleration (a) = gradient
For acceleration-time (a-t) graphs; velocity (v) = area
Algebraic description of motion: constant acceleration equations of motion.
v = u + a t x = displacement, v = instantaneous velocity = x/t
x = ½(u + v)t u = initial velocity, vav =average velocity = ½(u + v)
x = ut + ½at2 v = final velocity, v = change in velocity = (v – u)
x = vt – ½at2 a = acceleration = v/t = vav /t ,
v2 = u2 + 2ax t = time interval of constant acceleration, t = time interval of change
N1: “A body continues in its state of rest or constant motion unless acted on by a net external force”
Iff F = 0, v=0. If and only if no net external force acts on an object then its velocity will not change
N2: “The net external force changes the velocity of an object in proportion to its mass”
F = ma = p/t. The net force on an object is proportional to its rate of change of momentum
N3: “Every action has an equal & opposite reaction”
FAB = -FBA. The force of an object on another is equal & opposite to the force of the second onto the first
Newton’s Laws assume that physical quantities such as mass, time, & distance are absolute quantities. This means that their values did not change whatever the frame of reference.
Apply Newton’s laws to situations with a few forces in one & two dimensions
F = F1 + F2 , for two forces acting on an object (or system)
Use N1 to determine if an object is in equilibrium (F = 0), if so a=0, & e.g., F1 = -F2., if not use N2
Use N2 to relate force, mass, acceleration (changes in velocity), changes in momentum and time
Use N3 only to find the forces of one object on another...