PPMF101

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PPMF101 Lecture 4

• Motions in 1 2 Dimensions

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Vector Scalar quantity

• Vector
• A quantity that has magnitude and direction.
• Eg. Displacement,
• velocity, acceleration, force, momentum,
  impulse, weight, friction, tension, electric and
  magnetic field.

• Scalar
• A quantity that has magnitude only.
• Eg. Distance, speed, pressure, energy, heat,
  work, power, time, charge and temperature.

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Distance Displacement

• Distance
• Scalar quantity
• Magnitude only

• Displacement
• Vector quantity
• Magnitude and direction

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Speed

• Speed refers to how far an object travels in a
  given time interval, regardless of direction.
• A scalar quantity.

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velocity

• Velocity is used to signify both the magnitude
  (numerical value) of how fast an object is moving
  and the direction in which it is moving.
• A vector quantity.

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Instantaneous velocity

• Instanteneous velocity at any moment is defined
  as the average velocity over an infinitesimally
  short time interval.

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Acceleration

• Acceleration specifies how rapidly the velocity
  of an object is changing.
• If velocity is increasing it is called
  acceleration.
• If velocity is decreasing it is called negative
  acceleration or deceleration.

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Instantaneous acceleration
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Graph displacement (s) vs time (t)

• Slope velocity

s
s
t
t
zero velocity
constant velocity
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Graph displacement (s) vs time (t)
s
s
t
t
decreasing velocity
increasing velocity
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Graph velocity(v) vs time(t) (p.25)

• Slope acceleration
• Area under the graph distance travelled

v
v
t
velocity increasing uniformly constant
acceleration
t
constant velocity zero acceleration
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Graph acceleration(a) vs time(t)

• For constant acceleration.
• The graph is a straight horizontal line.

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v vs t s vs t graphs braking distances
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S vs t v vs t graphs catching a speeder (p.31)
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Equations of motion

• Constant acceleration due to gravity g

• Constant acceleration a

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Examples

• 1. A runner leaves the starting blocks and
  accelerates at 2.50 m/s2 for 4.00 s. What
  speed does the runner reach?
• 2. An airplane that is flying level needs to
  accelerate from a speed of 200 m/s to a speed of
  240 m/s while it flies a distance of 1200 m.
  What must the acceleration of the plane be?

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• 3. A rock is dropped from a vertical cliff. The
  rock takes 7.00 s to reach the ground below the
  cliff. What is the height of the cliff?
• 4. If an object was freely falling, from what
  height would it need to be dropped to reach a
  speed of 70.0 m/s before reaching the ground?

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Eg. 1

• Determine the average velocity for
• (i) the first 3 seconds
• (ii) the entire motion

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Eg. 2

• This is a graph for a moving object.

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Eg. 2 continue

• (i) Explain the motion at PQ and RS.
• (ii) What is the total displacement of the
  object?
• (iii) What is the time for the motion of the
  object?
• (iv) Determine its average velocity.
• (v) What is its acceleration at
• t 22 s?

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Eg. 3

• A car is driven from point O at the north with
  velocity 60 km/h for 10 min until it reached a
  junction, S. The car then turn west and moved
  with a velocity of 30 km/h for another 10 min
  until its reached point A. Determine
• (a) the average speed of the car from O to A.
• (b) the average velocity of the car from O to A.

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Eg. 4

• A mouse deer runs a distance of 70 m between two
  points at a constant acceleration in 7.0 s. Its
  velocity while passing through the second point
  is 15.0 m/s.
• (a) What is its speed at the first point?
• (b) What is the acceleration of the mouse deer?

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Projectile Motion
A projectile is an object moving in two
dimensions under the influence of Earth's
gravity its path is a parabola.
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Projectile Motion
If an object is launched at an initial angle of
?0 with the horizontal, the analysis is similar
if ?0 0 launched from certain height, except
that the initial velocity has a vertical
component.
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Projectile Motion
It can be understood by analyzing the horizontal
and vertical motions separately.
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Projectile Motion
The speed in the x-direction is constant in the
y-direction the object moves with constant
acceleration g. This photograph shows two balls
that start to fall at the same time. The one on
the right has an initial speed in the
x-direction. It can be seen that vertical
positions of the two balls are identical at
identical times, while the horizontal position of
the yellow ball increases linearly.
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Projectile Motion

• Projectile motion is motion with constant
  acceleration in two dimensions, where the
  acceleration is g and is downward.

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Solving Problems Involving Projectile Motion
Example 3-6 Driving off a cliff. A movie stunt
driver on a motorcycle speeds horizontally off a
50.0-m-high cliff. How fast must the motorcycle
leave the cliff top to land on level ground
below, 90.0 m from the base of the cliff where
the cameras are? Ignore air resistance.
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Projectile Motion
metal grinding
Examples of projectile motion. Notice the effects
of air resistance.
Water fountain
fireworks