Post on 06-Mar-2016
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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)
A straight road marked with numbers:
Straight line motions
1
2
34
forward0
Move forward 4 m (or +4 m)
Start point (zero point)
A straight road marked with numbers:
1
2
34
forward
Straight line motions
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
Average velocity during 100-200 s
Example 5
= 0
slope of 100-200 s = 0
Average velocity during 200-300 s
Example 5
= displacement of 200-300 s
time of 200-300 s
= 50
100
= 0.5 m s-1
Average velocity during 300-400 s
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