phy- motion graph analysis

Graphs of straight line motion

A Slope =

B Slope =

C Slope =

D Slope =

t

vu

t

uv

uv

t

vu

t

1 Which is correct about the graph?

velocity

time

u

v

t

2 The displacement of an object atdifferent times is recorded:

Displacement s / m Time t/s

0

2

4.5

10

0

1

2

4

A The object moves with a constantvelocity.

B The object is accelerating.

C The object is decelerating.

2 Which of the following statements aboutthe motion of the object is correct?

43 When an object is moving at a uniformspeed of 4 m s1 ,

it travels _______ m in each second.

A straight road marked with numbers:

1

2

34

forward

Straight line motions

0Start point (zero point)



1

2

34

forward0

Move forward 4 m (or +4 m)

Start point (zero point)


1

2

34

forward


0Start point (zero point)

-4

-3

-2-1

backwardMove backward 4 m (or -4 m)

Motion graphs

how far body moves

(displacement)

Motion graphs tell you

how fast it moves

how speed changes

time

displacement / m

A displacement-time graph or s-t graph ()

Displacement-time graph

gives the displacement of a moving object at different times.

Consider: A car is travelling at a constantor uniform velocity of 10 m s1.

moves 10 m every 1 s

1 Displacement-time graph

s / m

t/s0 41 2 3

10

20

30

40

Slope of s-t graph

The slope of the s-t graph gives the velocity of the body.

slope =

s

tt1 t2

s2

s1s2 s1t2 t1

= velocity

A velocity-time graph or v-t graph

()

2 Velocity-time graph

gives the velocity of a moving object at different times.

The v-t graph for the car travelling at a constant velocity of 10 m s1:

v/m s1

t/s

10a horizontal line: the

velocity stays the same all the time.

2 Velocity-time graph

The slope of the v-t graph gives the

acceleration of the body.

a Slope of v-t graph

v

tt1 t2

v2

v1

slope = v2 v1t2 t1

= acceleration

The v-t graph is a horizontal line

the car is travelling at an unchangedvelocity

with no acceleration

it has a zero slope

a Slope of v-t graph

v/m s1

t/s

10

The area under a v-t graph is the displacement

(s) during the time interval.

b Area under v-t graph

v

t0

This area= displacement

(i) A butterfly flies with a velocity v for a time t.

t

v t

v

area = v t

v

tt

s = v t

Explanation:

(ii) A butterfly flies with 3 different velocities.

s = v1 t + v2 t +v3 t

t

v3 t

v3

t

v2 t

v2

t

v1 t

v1

A1=v1 t

v

tt t t

A2=v2 t A3=v3 t

(iii) A butterfly flies with n different velocities.

s = v1 t + v2 t +...+vn t

tt t t

t t

vn t

vn

v2 t

v2

t

v1 t

v1

A1=v1 t

v

A2=v2 t An=vn t

(iv) A butterfly flies with various velocities.

v

total displacement = area under graph

t

v

A car travels on a road as shown.

(Q1-4) A car travels...

45 m

(Q1-4) A car travels...s-t graph of the car from a traffic light

1 2 3 4 5t / s

s / m

10

20

30

40

45 m

A The car passes by the traffic light when t = 0 s.

B The car moves with a uniform velocity in the first 3 seconds.

C The car accelerates between t = 3 s and t = 4 s.

D The car stops after 5 seconds.

Q1 Which of the following...

Which of the following statements is correct?

1 2 3 4 5t

s

A 9 m s1

B 10 m s1

C 15 m s1

D 30 m s1

Q2 The velocity...

The velocity of the car at t = 2 s is

1 2 3 4 5t / s

s / m

10

20

30

40

25

Q3 The car is...

The car is _____ m away from the traffic light at t = 1.5 s.

1 2 3 4 5t / s

s / m

10

20

30

40

Q4 True or false...

The car passes the tree before it stops.

(T/F)

1 2 3 4 5t / s

s / m

10

20

30

40

45 m

The acceleration-time graph or a-t graph ()

3 Acceleration-time graph

gives the acceleration of the car atdifferent times.

The a-t graph for the car travelling at a constant velocity of 10 m s1:

a/m s2

t/s

Acceleration = 0 m s2

3 Acceleration-time graph

The graph is exactly zero all thetime...

since the car is moving at constant velocity: zero acceleration.

Car A moves at uniform velocity (slope)

moves 10 m every 1 s

4 Other motions

displacement/m

time/s

constant slope

constant slope

constant slope

uniform / constant v

slopes 0)(2

m 0)(20

= 10 m s1

= velocity

Car A

Displacement-time graph

In 5 s, car B moves a greater displacement.

car B moves faster than Aslope: graph (ii) > graph (i)

slope of s-t graph is velocity

m

A

m

B

Car BCar As/m s/m

t/s t/s

v2 > v1

Car C

accelerates!!

v2

v1

s/m

t/s

4 Other motions

Car D

Slope (velocity) = 0

remains stationary at 50 m

s/m

t/s

4 Other motions

s-t and v-t graphs

Car A

s/m

t/s t/s

uniform velocity!

v / m s1

Car C

s/m

t/s t/s

v/m s1

s-t and v-t graphs

Car D

s/m

t/s

t/s

slope = 0Slope of s-t

graph = 0 = v

v/m s1

s-t and v-t graphs

1

2

3

4

Car E

t/s

v/m s1

t/s

a/m s2

uniform a

slope = acceleration

v-t and a-t graphs

t/s

v/m s1

t/s

a/m s2

Car A

Car B

Car C

Car C

Car B

Car A

no change in v

All slopes 0 !

no change in v

v-t and a-t graphs

Conclusion

the higher is the velocity of the body.

The larger the slope of a s-t graph,

The slope of a s-t graph gives the velocity.

The slope of an v-t graph gives the acceleration.

5 Graphs of motion with a change

in direction

Car E is travelling at a constant velocity of 10 m s-1.

It then decelerates to rest,

reverses direction,

accelerates for a short time...

Car E

v / m s1

1

2 3 4 50

5

10

5

10

t/s

t = 0 to t = 2 sconstant v of

10 m s1 accelerates ata = 20 m s2

(decelerates)

t = 2.5 sat rest

accelerates ata = 20 m s2 (in opposite direction)

constant v of 10 m s1

A displacement-time graph of a boywalking along a straight road.

(a) Describe his motion.

Example 5

(a)

Example 5

0-100 s: uniform velocity

100-200 s: at rest300-400 s: at rest

0 100 200 300 400

100

200

distance / m

200-300 s: smaller uniform velocity

Total displacement travelled = 150 m

150

(b)(i) Calculate the total displacement travelled.

Example 5

0 100 200 300 400

100

200

distance / m

time / s

(b)(ii) Calculate the average velocity during the time intervals 0-100 s, 100-200 s, 200-300 s and 300-400 s.

Example 5

0 100 200 300 400

100

200

distance / m

time / s

Average velocity during 0-100 s

Example 5

= displacement of 0-100 s

time of 0-100 s

= 100

100

= 1 m s-1


Example 5

= 0

slope of 100-200 s = 0


Example 5

= displacement of 200-300 s

time of 200-300 s

= 50

100

= 0.5 m s-1


Example 5

= 0

slope of 300-400 s= 0

(b)(iii) Calculate the average velocity during whole journey (0-400 s).

Example 5

Average velocity during whole journey

= total displacement

total time= 0.375 m s-1=

150

400

The figure shows the v-t graph of a car travelling along a straight road.

Example 6

velocity / m s1

time / s

15

10

5

020 50 60

(a) What is its acceleration during the time intervals represented by OA, AB and BC?

For OA, the car accelerates uniformly.

Acceleration = slope

For AB, the car travels at a uniform velocity of 15 m s1.

= 0.75 m s2020

015

=

Example 6

Acceleration = 0

For BC, the car decelerates uniformly.

Acceleration = slope

= 1.5 m s25060

150

=

Negative acceleration means deceleration.

Example 6

(b) What are the displacements during each time interval?

Displacement is the area under the graph.

Example 6

velocity / m s1

time / s

15

10

5

020 50 60

For AB:

displacement = 15 30 = 450 m

For OA:

displacement = 15 20 = 150 m2

1

For BC:

displacement = 15 10 = 75 m2

1

Example 6

(c) What is the average velocity for the whole

journey?

Overall displacement = 150 + 450 + 75 = 675 m

Total time taken = 60 s

Average velocity for the whole journey

= taken time total

ntdisplaceme overall

60

675=

= 11.25 m s1

Example 6

A car moving on a road has oil leakage. Oil drips out drop by drop steadily and leaves some dirt marks on the road.

Q1 A car moving...

v / ms1

t/s

Q1 Which of the following...Which of the following dirt mark patterns iscorrect? v

t

A

B

C

Stop at here and change direction!

Q2 In a race...

In a race, 2 runners X & Y start at time t = 0.

v

t10

Y

X

Q2 In a race... Which picture is correct?

v

t10

Y

X

A

X Y

B

X Y

C

XY

at

Q3 True or false...

The figure describes something moving in one direction only.

(T/F)

Q4 True or false...

The figure shows that an objects deceleration is greater than its acceleration.

(T/F)

v

t

The End

phy- motion graph analysis

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