Lecture 5: Introduction to Physics PHY101

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Lecture 5 Introduction to Physics PHY101

• Chapter 2
• Distance and Displacement, Speed and Velocity
  (2.1,2.2)
• Acceleration (2.3)
• Equations of Kinematics for Constant
• Acceleration (2.4)

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Displacement and Distance

• Displacement is the vector that points from a
  bodys initial position, x0, to its final
  position, x. The length of the displacement
  vector is equal to the shortest distance between
  the two positions.
• ?x x x0
• Note
• The length of ?x is (in general) not the same as
  distance
• traveled !

3
Average Speed and Velocity

• Average speed is a measure of how fast an object
  moves on average
• average speed distance/elapsed time
• Average speed does not take into account the
  direction of
• motion from the initial and final position.

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Average Speed and Velocity

• Average velocity describes how the displacement
  of an object changes over time
• average velocity displacement/elapsed time
• vav (x-x0) / (t-t0) ?x / ?t
• Average velocity also takes into account the
  direction of
• motion.
• Note
• The magnitude of vav is (in general) not the
  same as the
• average speed !

5
Instantaneous Velocity and Speed

• Average velocity and speed do not convey any
  information about how fast the object moves at a
  specific point in time.
• The velocity at an instant can be obtained from
• the average velocity by considering smaller
  and smaller time intervals, i.e.
• Instantaneous velocity
• v lim ? t-gt 0 ?x / ?t
• Instantaneous speed is the magnitude of v.

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Concept Question

• If the average velocity of a car during a trip
  along a straight road is positive, is it possible
  for the instantaneous velocity at some time
  during the trip to be negative?
• 1 - Yes
• 2 - No

correct
If the driver has to put the car in reverse and
back up some time during the trip, then the car
has a negative velocity. However, since the car
travels a distance from home in a certain amount
of time, the average velocity will be positive.
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Acceleration

• Average acceleration describes how the velocity
• of an object moving from the initial position
  to
• the final position changes on average over
  time
• aav (v-v0) / (t-t0) ?v / ?t
• The acceleration at an instant can be obtained
  from
• the average acceleration by considering
  smaller and smaller time intervals, i.e.
• Instantaneous acceleration
• a lim ? t-gt 0 ?v / ?t

8
Concept Question

• If the velocity of some object is not zero, can
  its acceleration ever be zero ?
• 1 - Yes
• 2 - No

correct
If the object is moving at a constant velocity,
then the acceleration is zero.
9
Concept Question

• Is it possible for an object to have a positive
  velocity at the same time as it has a negative
  acceleration?
• 1 - Yes
• 2 No

correct
An object, like a car, can be moving
forward giving it a positive velocity, but then
brake, causing deccelaration which is negative.
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Kinematics in One DimensionConstant Acceleration

• Simplifications
• In one dimension all vectors in the previous
  equations
• can be replaced by their scalar component along
  one axis.
• For motion with constant acceleration, average
  and
• instantaneous acceleration are equal.
• For motion with constant acceleration, the rate
  with which
• velocity changes is constant, i.e. does not
  change over time.
• The average velocity is then simply given as
• vav (v0 v)/2

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Kinematics in One DimensionConstant Acceleration

• Consider an object which moves from the initial
  position x0, at time t0
• with velocity v0, with constant acceleration
  along a straight line.
• How does displacement and velocity of this object
  change with time ?
• a (v-v0) / (t-t0) gt v(t) v0 a
  (t-t0) (1)
• vav (x-x0) / (t-t0) (vv0)/2 gt x(t)
  x0 (t-t0) (vv0)/2 (2)
• Use Eq. (1) to replace v in Eq.(2)
• x(t) x0 (t-t0) v0 a/2 (t-t0) 2
  (3)
• Use Eq. (1) to replace (t-t0) in Eq.(2)
• v2 v02 2 a (x-x0 ) (4)

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Summary of Concepts

• kinematics A description of motion
• position your coordinates
• displacement ?x change of position
• velocity rate of change of position
• average ?x/?t
• instantaneous slope of x vs. t
• acceleration rate of change of velocity
• average ?v/?t
• instantaneous slope of v vs. t