Motion in One Dimension

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Motion in One Dimension

• Average velocity

x1
x2
Displacement
t1
t2
Average velocity is defined as
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Motion in One Dimension

• Instantaneous velocity

Is the velocity of the object at any point in
time.
We call this the limit at which the change in
time approaches zero or The rate of change of
displacement with respect to time.
Velocity is a vector quantity. That is, it has a
magnitude and direction.
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Motion in One Dimension

• Acceleration

Similarly, acceleration is defined as
When the velocity varies linearly with time,
acceleration becomes constant
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Motion in One Dimension

• Other ways of writing the previous equations

or
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Motion in One Dimension

• Under constant acceleration the following
  equations can be derived.

Eqn 1.
Eqn 2.
Eqn 3.
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Motion in One Dimension

• Exercise Derive the equations on the previous
  page

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Motion in One Dimension

• Exercise A car accelerates from 60 km/hr to 100
  km/hr in 4 s.
• What is the distance that it travelled during
  this time? Take the direction of motion to be
  positive.

What do we know?
Initial velocity v0 60 km/hr 16.7 m/s
Final velocity v 100 km/hr 27.8 m/s
Time t 4 s
What do we need to find?
Distance x
Use equation
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Motion in One Dimension

• Exercise A car speeding at 80 km/hr in a 60
  km/hr zone passes a still police car which
  immediately takes off in hot pursuit. Assuming
  that speeding car is moving at constant speed.
  Calculate how long it will take it will take for
  the police car to catch up to the speeding car
  and the speed of the police car at this moment.

Answer time taken is 16 s the speed at this
time is 160 km/hr
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Motion Under Gravity

• Gravity is a special case of 1D motion.
• Neglecting air friction, all objects near the
  earths surface will experience the same
  acceleration towards the centre of the earth.

Acceleration due to gravity is 9.8 m/s2
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Motion Under Gravity

• Example A ball is thrown vertically upwards from
  the roof of a 50 m building with a velocity of 20
  m/s. On its way down, the ball just misses the
  roof and falls to the ground.

What is the maximum height which the ball reaches?
x
What do we know?
Initial velocity v0 20 m/s
Final velocity v 0 m/s at max height
Acceleration a -9.8 m/s2
Use eqn.
50m
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Motion Under Gravity

• Example A ball is thrown vertically upwards from
  the roof of a 50 m building with a velocity of 20
  m/s. On its way down, the ball just misses the
  roof and falls to the ground.

How long does it take to hit the ground?
What do we know?
x
Initial velocity v0 20 m/s
Final velocity v 0 m/s at max height
Acceleration a -9.8 m/s2
Height above roof x 20.4 m
50m
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Motion Under Gravity

• Method 1. Calculate the time taken from roof to
  max. height, then time taken from max. height to
  ground.

From roof to max. height
x
From max. height to ground
50m
Total time is 5.8 s
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Motion Under Gravity

• Method 2. Take the roof as the initial position
  and the ground as the final position.

What do we know?
Initial velocity v0 20 m/s
Final velocity v ?
Acceleration a -9.8 m/s2
x
Distance traveled x -50 m
50m
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Motion Under Gravity

• Exercise A ball is dropped from a tower 70 m
  high. How far will it have fallen after 1.00s,
  2.00 s and 3.00 s?

Answer at 1.00 s distance is 4.9 m at 2.00
s distance is 19.6 m at 3.00 s
distance is 44.1 m