Everything Science Grade 10

CHAPTER 21. MOTION IN ONE DIMENSION 21.2

Distance is the length of dashed line. It is
how far you have to walk along the path from
the school to the shop.

b b

Start

(School)

Finish

(Shop)

DEFINITION: Displacement

Displacement is the change in an object’s position. It is a vector that points

from the initial position (~xi) to the final position (~xf).

Quantity: Displacement (∆~x) Unit name: metre Unit symbol: m

The displacement of an object is defined as its change in position (final position minus
initial position). Displacement has a magnitude and direction and is therefore a vector. For
example, if the initial position of a car is~xiand it moves to a final position of~xf, then the
displacement is:
∆~x=~xf−~xi

To help visualise what the displacement vector looks like think back to the tail-to-head
method. The displacement is the vector you add to the initial position vector to get a vector
to the final position. However, subtracting an initial quantity from a final quantity happens
often in Physics, so we use the shortcut∆to meanfinal - initial. Therefore, displacement
can be written:

∆~x=~xf−~xi

The following diagram illustrates the concept of displacement:

(^0) ~xi ~xf
∆~x
For example, if you roll a ball 5 m along a floor, in a straight line, then its displacement is
5 m, taking the direction of motion as positive, and the initial position as 0 m.
Tip
The wordsinitialand
finalwill be used very
often in Physics. Ini-
tialrefers to the sit-
uation in the begin-
ning of the descrip-
tion/problem and fi-
nalto the situation at
the end. It will often
happen that the final
value is smaller than
the initial value, such
that the difference is
negative. This is ok!
Displacement does not depend on the path travelled, but only on the initial and final
positions. We use the worddistanceto describe how far an object travels along a particular
path.
Physics: Mechanics 393