Equations of motion

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Equations of motion
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1 Which graphs does NOT represent motions of
constant acceleration?
a
v
t
t
s
v
?
t
t
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2 What does the area under a v-t graph represent?
displacement
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3 A car travelling in the ve direction speeds
up.
The sign of its velocity and acceleration should
be _________ and __________ respectively.
negative
negative
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1 Uniformly accelerated motion
A body accelerates uniformly from 8 m s1 to 16 m
s1 in 4 s.
constant slope its acceleration is constant
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1 Uniformly accelerated motion
Velocity increases
(16 8) 8 m s1 in 4 s
Acceleration slope 2 m s2
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1 Uniformly accelerated motion
the area under v-t-graph
Displacement
velocity/m s1
16
i.e. (8 16) 4/2 48 m
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8
4
0
time/s
1
2
3
4
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2 Equations of motion
Condition
Uniform acceleration
Slope
a
v u at
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2 Equations of motion
Area under graph
displacement
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2 Equations of motion
Area under graph displacement
2as (u v)(u v)
v 2 u 2 2as
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2 Equations of motion
Equations
Remarks
Signs of s, v, u and a should be clearly and
consistently specified.
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Example 8
The car is driven at 60 km h1.
the car skids to stop
Braking is then applied.
Find the deceleration of the car assuming it to
be uniform.
wheels are locked ? prevented from turning
Press ltEscgt to quit this example.
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Example 8
u 60 km h?1
16.7 m s1
s 28.5 m
v 0
Applying v 2 ? u 2 2as
a ?4.89 m s2
deceleration!
Press ltEscgt to quit this example.
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Example 9
A BMW 328Ci accelerates from rest at 3.8 m s2
for 7.3 s.
Calculate the velocity reached and the distance
travelled after 7.3 s.
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Example 9
v u at
0 3.8 ? 7.3
27.7 m s1
101 m
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(For questions 1 and 2.)
A boy rides a bicycle along a straight road.
He slows down at a constant rate of 2 m s2 for 8
s until he stops.
t 0 s
t 8 s
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Q1 Which of the following...
Which of the following sets of values is provided
by the above description?
s / m ? ? ? ?
u / m s-1 2 ? 0 ?
v / m s-1 0 0 ? 0
a / m s-2 ? 2 2 2
t /s 8 8 8 8
A B C D
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Q2 In order to find the initial...

• In order to find the initial velocity of the boy,

which of the following equations should be used?
A v u at B v2 u2 2as C D
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Q3 From t1 to t2, the car...
From time t1 to t2, the car accelerates
NON-UNIFORMLY from v1 to v2 and travels a
distance d.
t t1
t t2
The average velocity v of the car is (v1v2)/2.
(T/F)
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Q1 A golf ball is hit with an...
A golf ball is hit with an initial velocity of 3
m s1 towards the hole.
The golf decelerates uniformly at 0.5 m s2.
Can the golf ball reach the hole?
8 m
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Q1 A golf ball is hit with an...
u 3 m s1
a ?0.5 m s2
Can the golf ball reach the hole?
A v u at 0 3 ? 0.5t ? t 6 Yes, and
it takes 6 s to reach the hole.
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Q1 A golf ball is hit with an...
u 3 m s1
a ?0.5 m s2
Can the golf ball reach the hole?
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Q1 A golf ball is hit with an...
u 3 m s1
a ?0.5 m s2
Can the golf ball reach the hole?
C v 2 u 2 2as 02 32 2 ? 0.5 ? s ?
s 9 m Yes, because its maximum displacement gt
8 m if there were no hole.
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Q1 A golf ball is hit with an...
u 3 m s1
a ?0.5 m s2
Can the golf ball reach the hole?
A v u at ? t 6 s
C v 2 u 2 2as ? s 9 m
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Q2 The v-t graph of a...
The v-t graph of a badminton shuttlecock.
Can we use the equation of motion to study the
motion of the badminton?
A Yes. B No, because the badminton is not
accelerating. C No, because the acceleration is
not uniform.
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Q3 Compared with stopping on...
Compared with stopping on a dry road, a car
stopping on a wet road will have longer
___________ distance and ___________ distance.
braking
stopping
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Q4 True or false...
True or false The stopping distance will be
doubled if the deceleration of the car is halved.
(T/F)