warm up problem a bus travels 280 km south along a straight path with an average velocity of 24.4...

Warm up ProblemA bus travels 280 km south along a straight path with an average velocity of 24.4 m/s to the south. The bus stops for 24 min, then it travels 210 km south with an average velocity of 20.8 m/s to the south.

a. How long does the total trip last? b. What is the average velocity for the total trip?

Physics Honors B & A – Day 9/08 & 09/09/15

Motion in 1D cont.

Agenda•Acceleration?•velocity v. time plots•Kinematic equations•examples

What is acceleration?

Acceleration•Acceleration measures the change in velocity per time

•Units

•Acceleration is a vector•Positive or negative means left or right direction

Acceleration• Direction of acceleration will affect the magnitude and direction of

velocity. • Depending on Velocity vector, it could cause speeding up or

slowing down.

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Acceleration• Direction of acceleration will affect the magnitude and direction of

velocity. • Depending on Velocity vector, it could cause speeding up or

slowing down.

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Acceleration• Direction of acceleration will affect the magnitude and direction of

velocity. • Depending on Velocity vector, it could cause speeding up or

slowing down.

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Acceleration• Direction of acceleration will affect the magnitude and direction

of velocity. • Depending on Velocity vector, it could cause speeding up or

slowing down.

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Acceleration+v and +a speed up+v and –a slow down

-v and –a speed up-v and +a slow down

v = 0 and + a speed up in direction of av = 0 and –a speed up in direction of a

+ v and a = 0constant velocity (No change)-v and a = 0constant velocity (No change)

Acceleration•Recall rate of change in velocity

•Slope

If velocitywent on the y-axis

𝑣

𝑡And t went on the x-axis

Velocity v. time plot

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Velo

city

(m/s

)

Velocity v. time plot

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Velo

city

(m/s

)

Use

𝑡1

v  1

v  2

Velocity v. time plot

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Velo

city

(m/s

)

𝑡1

v  1

𝑡 2

v  2

So… •How would you get from a position v. time plot to acceleration v. time plot?

and vice versa?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Positi

on (m

)

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Velo

city

(m/s

)

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Acce

lera

tion

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

Time (s)

Positi

on (m

)

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Time (s)

Velo

city

(m/s

)

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Acce

lera

tion

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

35

Time (s)

Positi

on (m

)

What would be ?

Determine acceleration and velocity vs. time plot from Position v. time plot

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

Time (s)

Velo

city

(m/s

)

What would be ?

Determine Position v. time plot from Acceleration vs. time plot

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

Time (s)

Acce

lera

tion

(m/s

2)

What would be ?

Trends between position, velocity and acceleration -

• What about the word problems?

Kinematic Equations

•All equations valid for constant acceleration

Example•A car with an initial speed of +4.0 accelerates uniformly at a rate of +3.0 . Find the final velocity and the displacement after 5.0 s.

Draw a picture.Write down the given values. Write down what we are looking for.Write down the equation we need to use. Convert units.Manipulate equation. Input number with units. Calculate answer with correct units.Clearly mark answer.

Example

•A car accelerates uniformly from rest to a velocity of +23.7 m/s in 6.5 s. a) What was it’s acceleration? b) What was the car’s displacement?