9
The Change in a physical quantity
For any physical quantity such as the distance x , the change in x is written as Δ x x f x i (always the
final value – initial value). The symbol Δ (or delta), a Greek letter, representing a change, and x f , x i are
the final and the initial (starting) values of the quantity x respectively. Figure (1.4) shows an object
changing its position during a time of travel t t f t i
.
1
1
x 0
xi
xf
Figure 1.4: During time interval t , the object (person and a car) changes its position by x.
The average speed can, therefore, be written as
v
x x f xi
t
t
(1.2)
1.4.2 Velocity
Velocity v is how fast or slowly an object changes its displacement (position). The displacement D is a
vector quantity, which tells us both the distance traveled by the object as well as the direction of motion.
From this we conclude that velocity is a ratio of displacement (not distance) over time and, therefore, it is
a vector quantity. The average velocity is written as
velocity
displacement
, or
time to cover that displacement
D
v
t
(1.3)
Example 1.4
A man starts moving from home (origin (0)) and walks 6m east (to the right), stopped and found that he
forgot his wallet at home. Therefore, he rushed backward (west) heading home. If the total time of his
walk both ways is 2min then find (a) his average speed and (b) his average velocity.
Solution
(a) v
12m
total distance traveled
v
0.1m / sec
2 60 sec
total time