Linear Motion
Physics: Chapter 2
Mechanics
The study of motion
Kinematics: description of motion (text chapters 2,3, and 5)
Dynamics: Why motion happens (text chapter 4 and 5)
Relativity of Motion
All motion is relative to a frame of reference
Key part of solution is defining reference
Given as part of problem
You select
Frame of Reference Conventions
up and right - positive
down and left - negative
You may define others for ease of solution. Must clearly identify.
Definitions
Position: location wrt a reference point
Distance (x): separation between positions
Displacement (x): net change in position or shortest distance between two points
Speed
Rate of change of position
rate of change means divide by time
Symbol: v
Average Speed: total distance/total time
Unit: m/s
Problems
Read and understand problem
Draw diagram with reference frame
ID Concept/Formula: v = x/t
Solve for unknown
Substitute values and solve
Velocity
Vector quantity describing speed and direction
Relative to a frame of reference
Symbol: v or "v" with an arrow over it
text uses v, context determines if speed or velocity
v = (x - xo)/(t - to)
v = DxDt
Units: m/s
Problems
Read and understand problem
Draw diagram with reference frame
ID concept/formula: v = Dx/Dt
Solve for unknown
Substitute know values and solve
Instantaneous Velocity
Velocity at an instant in time
Very small Dx and Dt
v = limD(t®0) Dx/Dt
v given in problems assumed to be instantaneous
Position-Time
Velocity is constant
x = vt
independent: t
dependent: x
slope: v
Position-Time (2)
Slope is positive: velocity increases
Slope is zero: at rest
Slope is negative: Velocity decreases
Acceleration
Rate of change of Velocity
Positive: in direction of motion
Negative: opposite to motion
May affect either speed of direction
Deceleration
If v and a in opposite direction object slows down (decelerates)
A negative acceleration causes object to decelerate
Deceleration caused by negative acceleration
Acceleration
a = v - vo / t - to
a = Dv / Dt
Units: m/s2
Velocity after Acceleration
Add the effect of acceleration to initial velocity
v = vo + at
Constant Acceleration
Average velocity: mid-point of the velocity range
Displacement: average velocity times time
Derive formula for x if a is known and v is not
When time is Unknown
Use x = ½ (v + vo) t and
v = vo + at to find v without t
v2 = vo2 + 2ax
Velocity vs. Time
Time: independent; Velocity: dependent
Slope: = Dv/Dt = a
Area under line is displacement
area = ½ at2 = x
Position vs. Time
d = ½at2
a power function
graph will be parabolic
Slope of tangent = Dd/Dt = v
Solution of Motion Problems
Read problem carefully
ID variables and implied data
ID the concept relating the variables Diagram the problem
Solve for unknown variable
Substitute known values and solve
Is your answer reasonable?
concept
diagram
does it make sense (especially with square roots)
Acceleration and gravity
Galileo: all bodies fall with the same acceleration
Symbol: g
May substitute for a in formulas
x = vot + ½gt2
Symmetry of Falling Bodies
a = g (constant, gravity only force)
t up = t down
x same in equal times
v same at equal heights