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