LINEAR MOTION
LINEAR MOTION
Motion is Relative
Everything moves even though they may appear to be at rest
Frame of Reference
Allows you to measure changes in position.
A coordinate system for specifying the precise location of an object in space
Frame of Reference
This diagram shows a change in position along the x-axis.
What about the y-axis? How do I know?
Frame of ReferencePositive and negative changes depend upon the frame of reference
Displacement
Δx = xf - xiChange in position = final position – initial position
DisplacementDoes not always equal distance traveled
Displacement
DisplacementA teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
Even though the teacher has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m). Yet when she is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m).
Displacement ExampleThe diagram below shows the position of a cross-country skier at various
times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.
Determine the resulting displacement and the distance traveled by the skier.
Displacement ExampleConsider a football coach pacing back and forth along the sidelines. The diagram
below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In
other words, the coach moves from position A to B to C to D.
What is the coach's resulting displacement and distance of travel?
Scalar vs. Vector
Vectors
Can be represented graphically
Scalar vs. Vector Example
a. 5 m b. 30 m/sec, East c. 5 mi., North d. 20 degrees Celsius e. 256 bytes f. 4000 Calories
Determine whether the following are scalar or vector quantities.
scalarvector
scalarscalar
scalarvector
VelocityVelocity is a vector
Velocity
Velocity ExampleHeather and Matthew walk eastward with a speed of 0.98 m/s. If it takes them 34 min to walk to the store, how far have they walked?
Variables Equation Solve
v = 0.98 m/sΔt = 34 minΔd = ??
v = ΔdΔt
=v Δt Δd
Units don’t match!
34 min
1 min
60 s= 2040 s
=(0.98 m/s)(2040 s) Δd
= 1999.2 m = 2 km Δd
Instantaneous VelocityVelocity of an object at a specific point in its path
AccelerationChange in velocity over time
constant velocity
constant negative accelerationzero acceleration
constant positive acceleration
Acceleration
Acceleration is a vector!
Kinematics
Δx = vit + ½ at2
vf 2 = vi
2 + 2aΔx
Uniform Straight Line Acceleration
vf = vi + at