Quick QuizQuick QuizConsider 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 average speed and average velocity?

Representing Motion Representing Motion Using GraphsUsing Graphs

Position-Time Graphs

Velocity-Time Graphs

position-time graphsposition-time graphsa graph describing the motion of

an object, with position on the vertical axis and time on the horizontal axis

it is important to understand how the shape of a p-t graph relates to the motion it describes

straight line the object is covering an equal distance per time interval (constant motion)

curved line the distance covered each time interval is not consistent (non-uniform motion)

flat line no change in position over time (standing still)

steep line large change in position over time (moving quickly)

shallow line small change in position over time (moving slowly)

negative/downward line the object is travelling in a negative direction◦can be uniform or non-

uniform◦can be fast or slow

*Therefore, by looking at a position-time graph, one can determine:

1.the direction of movement2.the speed of the

movement (slow or fast)3.if the movement is uniform

(constant speed) or non-uniform (acceleration)

slopeslopeslope is the measure of the

steepness of a line slope = rise = Δd = d2 - d1

run Δt t2 – t1

the slope of a p-t graph yields the velocity of the object

the steeper the line, the greater the velocity (increased displacement in a given amount of time)

if the line remains level, then velocity is constant

exampleexampleexamine the

graph

choose 2 points on the line (x, y)

apply the formula:

velocity-time graphsvelocity-time graphsa graph describing the motion of an

object, with velocity on the vertical axis and time on the horizontal axis

useful when studying objects moving with constant velocity or constant accelerationpositive velocity positive

velocityzero acceleration positive

acceleration

shape of v-t graphsshape of v-t graphsshow direction:

show change in velocity (acceleration)

comparing p-t and v-t comparing p-t and v-t graphsgraphs

the following motion yields:

position-time graph velocity-time graph

CONSTANT VELOCITY (UNIFORM MOTION)

comparing p-t and v-t comparing p-t and v-t graphsgraphs

the following motion yields:

position-time graph velocity-time graph

CHANGING VELOCITY (NON-UNIFORM MOTION)

area of a v-t grapharea of a v-t graphfor a velocity-time graph, the

area bound by the line and the axes represents the displacement of the object

equations for area equations for area calculationscalculationsrecall the equations for

calculating the area of basic geometric shapes

note that the area of a trapezoid can be calculated by finding the sum of the areas of the contained rectangle and triangle

practicepractice

A = 30 m/s X 4 s A = 30 m/s X 3 s = 120 m = 90 m

practicepractice

A = ½ X 1 s X 10 m/s A = ½ X 3 s X 30 m/s

= 5 m = 45 m

practicepractice

A = ½ x 1s x (20+30 m/s) A = ½ x 2s x (30+10)

= 25 m = 40 m

Quick QuizQuick QuizConsider the graph at the right. The object

whose motion is represented by this graph is ... (include all that are true):

a)moving in the positive direction.b)moving with a constant velocity.c) moving with a negative velocity.d)slowing down.e)changing directions.f) speeding up.g)moving with a positive acceleration.h)moving with a constant acceleration.