Position, Distance and Displacement

Subject: 

Physics

Term:

FIRST TERM

Week:

WEEK 2

Class:

SS 2

Topic:

Position, Distance and Displacement

Previous lesson: 

The pupils have previous knowledge of

 Third Term Examinations SS 1 Examination Physics

that was taught as a topic in the previous lesson

Behavioural objectives:

At the end of the lesson, the learners will be able to

• say the meaning of
• give examples of various
• explain the importance of
• point out the need to

Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards

Methods of Teaching:

• Class Discussion
• Group Discussion
• Asking Questions
• Explanation
• Role Modelling
• Role Delegation

Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum
• Workbooks

Content:

WEEK TWO.

DATE…………….

TOPIC: Position, Distance and Displacement

CONTENT:

• Concept of position
• Location of point on a Cartesian plane
• Distance
• Estimation of distance between two point on a Cartesian plane
• Displacement
• Difference between distance and displacement
• Frame of reference

PERIOD ONE: POSITION

This is the location of a point/object with respect to a reference point. The position of a point in space is defined in terms of the distance of the point from the reference point (which is sometimes called ORIGIN). In physics, the position of an object in space is represented in a coordinate system. There are three main types of coordinate system for representing the position of an object in space:

Cartesian coordinate system:

This is also called the rectangular coordinate system. This consists of two (or three) mutually perpendicular axes. The Cartesian plane in two dimensions consists of two mutually perpendicular axes:

– the horizontal axis (also called the X axis or the abscissa) – the vertical axis (also called the Y axis or the ordinate).

The position of a point in this coordinate system is define in terms of it perpendicular distance from these axes.

For

instance

the

position

of

a

point

P

define

as

)

a,b

(

is

represented

as

shown.

axis

Y

–

0)

0

(

,

X-axis

a

b

(0,0) is the origin.

This is similar to the location of point on a graph sheet when plotting points.

CLASS ACTIVITY: locate the following point onthe graph sheet below. A(2,3) B(1,-1) C( 2,-3) D(-2,1) E(0, 2)

D

(-2,1)

A

(2.3)

Locate the remaining points.

EVALUATION: On a graph sheet, locate the following points

1. (2, -5)
2. (-3, -2)
3. (2.6, -3.4)
4. (-5.1, 6.3)
5. (2.76, 1.92)

PERIOD TWO:

DISTANCE.

This can be defined as the actual length measured along the path moved by an object. Distance is a scalar quantity and it S.I unit is metre (m). If an object moved along a straight line, the distance moved is the length of the straight line. If the path is a curve, then the distance moved is the length of the curve.

DISPLACEMENT:

This is the distance moved in a specified direction. Displacement is a vector quantity and its S.I unit is metre.

Estimation of displacement between two points on the Cartesian plane

Consider the point P and Q on a Cartesian plane. If the coordinate of P and Q is given as: P(x₁,y₁) and Q(x₂,y₂), then the displacement between P and Q on the Cartesian plane is given as

Example: Calculate the distance between the two points: P(4,2) and Q(1, 6)

Solution: P (x₁,y₁) Q (x₂, y₂)

P(4,2) Q(1,6)

X₁ = 4, Y₁ = 2 X₂ = 1, Y₂ = 6

Displacement between two points on the Cartesian plane

Consider the points P and Q on a Cartesian plane. If their coordinates are: P(x₁,y_1,z₁), Q(x₂,y_2, ), then the distance between P and Q on the Cartesian plane is given as

E.g: Calculate the distance between the points P(2, 0, 5) and Q(3, -2, 1)

Soln:

P(2, 0, 5) = ,

Q(3, -2, 1) = ,

D = 4.58units

Differences between distance and displacement

EVALUATION;

1. Calculate the distance between the following set of points.
   1. (2, 5) and (-4, -3)
   2. (8, 7) and (0, -8)
   3. (6, 6) and (-6, 1)
   4. ( -4, 14) and (8, 6)
2. The distance between the points (p, -2) and (3, -8) is 10units. What is the value of p?

PERIOD THREE:

frame of reference

This is a set of axes used to specify the position of object in space at any instant of time. For practical purposes, the frame of reference of the earthis taken to be at rest (i.e an inertia frame of reference). However, this is never so. In two dimensional continuums, the frame of reference consists of two axes.

object at any time in space.

x

y

z

In four dimensional continuums, the time coordinate is added to the space coordinate (x, y, z). Hence for three dimensional frames of reference position is defined as (x,y,z). But for four dimensional frame of reference, position is define as (x,y,z,t) – (space-time)

When an event in a frame of reference is observed in two frame of reference moving relatively with respect to each other, their observations will be different. This leads to the concept of relativity. (see Einstein theory of special relativity)

However, all frames of reference moving at a constant velocity with respect to each other are equivalent. All frames of reference at rest or moving with uniform velocity are called Galilean frames and that are equivalent for describing the dynamics of moving bodies.

EVALUATION

1. What is an inertia frame of reference?
2. What is a Galilean frame of reference?

GENERAL EVALUATION

1. The following are types of coordinate system except …. (a) rectangular coordinate system (b) cubical coordinate system (c) cylindrical coordinate system (d) spherical coordinate system
2. Another name for the horizontal axis of a Cartesian coordinate system is …. (a) Y-axis (b) ordinate (c) abscissa (d) coordinate
3. An ant on a graph page moved starting from the origin to another point (-6, 8). What is the displacement of the ant? (a) 4units (b) 7units (c) 9units (d) 10units
4. A rat on a horizontal frame of reference moved from (13, 7) metres to another point (x, 0) metres. For what value of x will the displacement of the rat be 25m? (a) 16 (b) 21 (c) 37 (d) 43
5. —- is the distance moved in a specified direction. (a) vector (b) displacement (c) distance (d) scala
6. A body moving with uniform acceleration a is represented by points (10, 30) and (25,

65) on a velocity-time graph. Calculate the magnitude of a. (a) 0.47ms^-2 (b) 0.50ms^-2

(c) 0.60ms^-2 (d) 1.67ms^-2 (e) 2.33ms^-2

Essay

1. Differentiate between distance and differences
2. Sketch a Cartesian plane and locate the following points on it.

(i) (-3, 4) (ii) (5, -2)

• 1. (4, 0)
  2. (1.2, -4.6)
  3. (5.72, 3.31)

WEEKEND ASSIGNMENT: what is the difference between an inertia frame of reference and a non-inertia frame of reference?

READING ASSIGNMENT: read pages 111-116 of the New School Physics by MW Anyakoha and answer question 7 and 8 on page 12

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise