Motion is Relative Everything moves even though they may appear to be at rest

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