# Scalars.

Physical quantities can be divided into two types namely:

i) Scalar quantity

ii) Vector quantity

A scalar quantity is physical quantity which has magnitude only.

Examples:

Mass, volume, time, temperature distance, pressure etc.

A vector quantity is a physical quantity which has both magnitude and direction.

Examples:

Velocity, acceleration, force, momentum displacement, Electric and magnetic field intensities.

Resultant Vector

A resultant vector is a single vector which produces the same effect on an object as two or more vectors acting on the same body.

Moving from O to B along OB is the same as moving through OA followed by AB. This shows that a single vector OB produces the same effect as adding;

In general the resultant force is calculated by adding all the force. But when the forces are in opposite direction the resultant force is calculated by subtracting.

The addition of vector takes place so long as the directions are the same though the magnitude may differ.

The subtraction occurs when the directions are opposite.

Example 1:

A goat moves 13m west and continue moving west ward 5m. Find the resultant displacement of the got .

Example 2:

Move 13m west and the move 5m east

Example 3:
Three force of 3, 5N and 7N act on an object A as shown. Find single vector which can produce the same effect.

Example 4

Three force of 3, 5N and 7N act on an object A as shown. Find single vector which can produce the same effect.

Example 5

Two force of 3 and 4N act on an object as shown. Find single force which can produce the same effect as the two forces above.

Solution:

Example 6

The figure below shows five forces acting on a 2.5kg mass.

Calculate the;
(i) resultant force on the mass
(ii) direction of the resultant force
(iii) acceleration of the mass

Solution
(i) FH =(12−7)N=5N→

FV ={(13+8)N−9N}=12N↓

Resultant Vector diagram

The magnitude of the resultant force

Using the Pythogras theorem;

Direction of the resultant force

From the Vector diagram;

(iii) Acceleration of the mass
From F=ma

Example 7

Two forces 6N and 8N act on 2kg body as shown. Calculate (i) the resultant force (ii) the acceleration