3.2.2 – Displacement | Physics with Mr Shone

Definition: Displacement
Displacement is the distance moved in a specific direction.

s is the symbol usually used to represent displacement.

Displacement is a vector. It indicates the body’s overall change in position.

e.g.: displacement, s = 3.0 m towards the right

Note
As displacement is a vector we must mention the direction when stating a value.

Representing Displacement

There are several ways to represent vectors:

1. Words:

s = 3.0 m towards the right

2. Symbols:

s = −5.0 m

(Assuming we have set up a sign convention, ie, to the right is positive, in which case this example would mean 5.0 m to the left)

3. Diagrams:

This would indicate the car being at the 20 m mark.

Example 1
A girl walks 5 km east and turns around and walks 3 km west. What is her displacement for the whole journey? Her displacement is 2 km east.

Example 1

A girl walks 5 km east and turns around and walks 3 km west. What is her displacement for the whole journey?

Her displacement is 2 km east.

Example 2
You walk 2 km to school in the morning and then 2 km home again in the afternoon. What is your total displacement for the whole day? Your displacement for the day is 0 km. *Obviously we do not need to state a direction here because the displacement is zero.*

Example 2

You walk 2 km to school in the morning and then 2 km home again in the afternoon. What is your total displacement for the whole day?

Your displacement for the day is 0 km.

Obviously we do not need to state a direction here because the displacement is zero.

Example 3
A boy runs 10 km north and then turns around and runs 7 km south. What is the magnitude of his total displacement for the whole journey? The magnitude of his displacement is 3 km. *We do not need to state a direction here because we are only asked for the magnitude of the* *displacement.*

Example 3

A boy runs 10 km north and then turns around and runs 7 km south. What is the magnitude of his total displacement for the whole journey?

The magnitude of his displacement is 3 km.

We do not need to state a direction here because we are only asked for the magnitude of the displacement.

Example 4
A student walks 5.0 km East from her home to school in the morning. After school, she walks 3.0 km North and another 2.0 km West to a park. Determine (a) her distance travelled, distance = length of red arrows distance travelled = 5 km + 3 km + 2 km = 10 km (b) her displacement. displacement is given by the purple arrow. length of this can be found from Pythagoras (√(3²+3²)) = 4.24 km Displacement is 4.24 km north-east of her home.

Example 4

A student walks 5.0 km East from her home to school in the morning. After school, she walks 3.0 km North and another 2.0 km West to a park.

Determine
(a) her distance travelled,

distance = length of red arrows

distance travelled = 5 km + 3 km + 2 km = 10 km

(b) her displacement.

displacement is given by the purple arrow.

length of this can be found from Pythagoras (√(3²+3²)) = 4.24 km

Displacement is 4.24 km north-east of her home.

Note
we can use the phrase north-east in the above example only because the direction was exactly half-way between north and east (ie at 45º). Other angles we would have to state the direction more explicitly and mention the angle.

Note

we can use the phrase north-east in the above example only because the direction was exactly half-way between north and east (ie at 45º).

Other angles we would have to state the direction more explicitly and mention the angle.

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