PHYSICS S.S ONE(SCALAR AND VECTORS) 1ST TERM

FIRST TERM : WEEK 5

TOPIC: SCALAR AND VECTOR QUANTITIES

SCALAR QUANTITIES:  They are quantities that have only magnitude (size) but no direction.

Example: length, time, speed, temperature, energy etc. note that all fundamental quantities are scalar quantities

VECTOR QUANTITIES: These are those which have both magnitude (size) and direction. Example are displacement, velocity, Acceleration, weight, force, momentum, electric Field. Note that all derived quantities are vector quantities.

POSITION

The position of an object in space or on a plane is the point at which the object can be located with reference to a given point, 0.  Position can be located using (x,y) or (x,y,z) Cartesians co-ordinate system i.e. locating two or more points or using bearing. When writing the co-ordinate of points, x is written first followed by y.

Example

Locate the following position on the  Cartesian plane:

(a) M  (2, 1.5);                         (b) L  (–3, 1.5);             (c) N (–2, –3).

DISTANCE; -Is the gap between positions or an origin. It is also defined as the separation or space between two points. Its S.I unit is metre.

To determine the distance between two points  A and B.

If 2 points A and B located in a plane are defined by two ordered pair of value (X1, Y1) and (X2, Y2) or assumed to be in space where they are defined by (X1, Y1, Z1) and (X2, Y2, Z2), the distance between them can be determined by applying the relation:

Distance, s =

EXAMPLE

Calculate the distance between the point M(2,3) and N(-5,1)

Solution

M(2,3) = (X1, Y1)

 N(-5,1) = (X2, Y2)

Distance, s =

Distance, MN =

Distance, MN =

Distance, MN=

Distance, MN=   = 7.3 units

DISPLACEMENT: This is defined as the distance travelled in a specific direction. It changes the position of an object. It requires distance and direction to specify it. Speed is the distance traveled per unit time or the rate of change of distance.
Speed = total distance traveled / time taken
Velocity is the speed in a given direction or the rate of change of displacement.
Average velocity = displacement/ time taken
Acceleration is the rate of change of velocity.
Acceleration = change of velocity / time taken
Change of velocity = final velocity (v) – initial velocity (u)
Acceleration = (final velocity – initial velocity) / time taken
  = (v – u) / t
Things to remember:
1. Constant velocity means the object is not accelerating. Acceleration is zero.
2. Constant acceleration means the object is increasing its velocity.

Example:- a car travels at an average speed of 50km/hr. what is the distance cover in 4mins

Solution:-

Distance = speed X time

Distance =  X 4 X 60 = 3333.3ms^-2

 PRESENTATION

Step I: The teacher introduces the topic to the students

Step II: The teacher explains position.

Step III: The teacher leads the students how to locate position on a Cartesians plane.

Step IV: The teacher defines distance and how to determine distance between two points.

Step V: The teacher explains displacement

Step VI: The teacher defines speed, velocity and acceleration.

EVALUATION

The teacher evaluates the lessons by asking the following questions:

1.       Define the position of an object

2.       Determine the distance between the points A(-5, 3) and C(4, 3)

3.       Define displacement.

4.      Differentiates between speed and velocity

ASSIGNMENT

1.       A man walks 5km east and 10km due North. Find the resultant displacement and the direction.

                [ans: 11.8km; N26.56^oE]

 

2.       A lorry starting from rest moves with uniform acceleration until it attain a speed of 108km/h after 15s. find its acceleration.

[ans: a=2ms^-2]