Bellringer

Compare and explain in complete sentences

what is distance.

Previous homework

Graph your motion distance, velocity, and

acceleration for your travel on a bus/car

from home to school and back

Homework

CALCULATE DISTANCE, VELOCITY AT ANY TIMEFOR

THE ARROW SHOOT VERTICALLY IN THE AIR

Graphing Motion

Every Picture Tells A Story

Position Time Graphs of Accelerated motion

Position vs. time graphs give you an easy and

obvious way of determining an objects

displacement at any given time, and a subtler way

of determining that objects velocity at any

given time.

A very useful aspect of these graphs is that the

area under the v-t graph tells us the distance

travelled during the motion.

Since the slope represents the speed, if the

speed is increasing over time, the slope must be

also be increasing over time. The graph is a

curve that gets steeper as you move along The

x-axis. A position-time graph for a ball in

free fall is shown below.

The graph of an object slowing down is also

cuved. The example below show the position-time

graph for a car coming to a gradual stop at a red

l ight. As time passes, the cars speed

decreases. The slope must therefore decrease.

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answers

Velocity vs Time Graphs

If the graph is a horizontal line, there is no

change in velocity, therefore there is no

acceleration (the slope is 0).

If the acceleration is positive then the slope is

positive (the line moves upward to the right).

If the acceleration is negative, then the slope

is negative (the line moves downward to the

right).).

Calculating acceleration from a velocity-time

graph

Calculating the distance on velocity-time graph.

An object is moving in the positive direction if

the line is located in the positive region of the

graph (whether it is sloping up or sloping down).

An object is moving in the negative direction if

the line is located in the negative region of the

graph (whether it is sloping up or sloping down).

If a line crosses over the x-axis from the

positive region to the negative region of the

graph (or vice versa), then the object has

changed directions.

The object moves in the direction at a constant

speed - zero acceleration (interval A). The

object then continues in the direction while

slowing down with a negative acceleration

(interval B). Finally, the object moves at a

constant speed in the direction, slower than

before (interval C).

The object moves in the direction while slowing

down this involves a negative acceleration

(interval A). It then remains at rest (interval

B). The object then moves in the - direction

while speeding up this also involves a negative

acceleration (interval C).

The object moves in the direction with a

constant velocity and zero acceleration (interval

A). The object then slows down while moving in

the direction (i.e., it has a negative

acceleration) until it finally reaches a 0

velocity (stops) (interval B). Then the object

moves in the - direction while speeding up this

corresponds to a - acceleration (interval C).

a plot of velocity versus time can also be used

to determine the displacement of an object. The

diagram below shows three different velocity-time

graphs the shaded regions between the line and

the time-axis represents the displacement during

the stated time interval.

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The velocity-time graph for a two-stage rocket is

shown below. Use the graph and your understanding

of slope calculations to determine the

acceleration of the rocket during the listed time

intervals. When finished, click the buttons to

see the answers.

20 m/s2

40 m/s2

-20 m/s2

Constant positive (rightward) velocity

Constant negative (leftward) velocity

Rightward velocity with rightward acceleration.

Rightward Velocity and negative acceleration

Leftward velocity, leftward acceleration

Leftward velocity rightward acceleration

Acceleration

- Acceleration the rate at which velocity is

changing - Acceleration ?v/ ?t
- Can increase or decrease (sometimes called

deceleration) - Think of traveling in a car, you can feel the

acceleration - 3 ways to accelerate in a car
- Brake pedalslowing down coming to a stop

(changing speed) - Steering wheelgoing around a corner or curve

(changing direction) - Gas pedalleaving from a stopped position

(changing speed)

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The object moves in the direction at a constant

speed - zero acceleration (interval A). The

object then continues in the direction while

slowing down with a negative acceleration

(interval B). Finally, the object moves at a

constant speed in the direction, slower than

before (interval C).

The object moves in the direction at a constant

speed - zero acceleration (interval A). The

object then continues in the direction while

slowing down with a negative acceleration

(interval B). Finally, the object moves at a

constant speed in the direction, slower than

before (interval C).

The object moves in the direction while slowing

down this involves a negative acceleration

(interval A). It then remains at rest (interval

B). The object then moves in the - direction

while speeding up this also involves a negative

acceleration (interval C).

- Zero to 90s - On this graph we see a horizontal

line that reads 5m/s for those same first 90

seconds. - On a v-t graph a flat line means constant

velocity. Constant velocity means zero

acceleration.

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Graphs of MotionUniform Velocity

- The area under a velocity vs time graph is the

displacement of the object. - Find the distance traveled by each object.

Acceleration

- Suppose you are traveling in a car and your speed

goes from 10.km/h to 60.km/h in 2.0s. What is

your acceleration? - Suppose a car goes from 80.km/h to 15km/h in 5.0

seconds. What is the acceleration? - A car is coasting backwards down a hill at a

speed of 3.0m/s when the driver gets the engine

started. After 2.5s, the car is moving uphill at

4.5m/s. Assuming that uphill is in the positive

direction, what is the cars average

acceleration?

Graphs of Motion

- Velocity vs time graphs How can you tell if the

object is accelerating or decelerating? - Accelerating (speeding up) when the magnitude

of the velocity is increasing - Decelerating (slowing down) when the magnitude

of the velocity is decreasing

Which pair of graphs shows the same motion?

Stage 1 The car moves forwards from the origin

to in the first 5 s.

Stage 2 The car moves backwards, passes the

origin, to in the next 5 s.

Stage 3 The car remains at rest in the last 5 s.

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What is the velocity for each stage of the

journey? b. What is the average (mean) velocity

for the whole journey

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Distance or Displacement

- Distancehow far an object has traveled
- Indianapolis is about 45 miles away
- The distance to Indianapolis is 45 miles the

distance back to Bloomington is 45 milesthe

total distance traveled round trip is 90 miles - Displacementhow far an object is from its

original position (direction matters) - The displacement to Indianapolis is 45 miles

north the displacement back to Bloomington is 45

miles souththe total displacement is 0 miles - You can find displacement by
- Finding the area under a velocity time graph
- Using the equation d vavg t

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Understanding the Connection Between Slope and

Velocity

The slope of a line for a distance vs. time graph

represents the velocity for the object in motion.

Slope can be determined using the following

formula

The change in y values divided by the change in x

values determines the average velocity for the

object between any two points.

- Pick two points on the line and determine their

coordinates. - Determine the difference in y-coordinates of

these two points (rise). - Determine the difference in x-coordinates for

these two points (run). - Divide the difference in y-coordinates by the

difference in x-coordinates (rise/run or slope).

rise over run

Calculate the velocity between 3 and 4 seconds.

Note This is a constant speed graph, so the

velocity should be the same at all points.

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