quick quiz consider a football coach pacing back and forth along the sidelines. the diagram below...
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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.