This document discusses motion in one dimension, including position and frames of reference, displacement and distance, speed and velocity, acceleration, graphs of motion, and equations of motion. It defines key terms like reference point, displacement, speed, velocity, acceleration, and describes the relationships between these quantities as expressed in equations and graphs. The document is intended as a lesson on motion in one dimension for a Grade 10 physics class.

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21. Motion in one dimension
Physics: Mechanics
Grade 10

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Position and frames of reference
A reference point is a point from where you take your measurements.
A frame of reference is a reference point with a set of directions.
Your position is where you are located with respect to your reference point.

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Displacement and distance
The displacement (Δx) of an object is how far it is from the reference point. It is the shortest
distance between the object and the reference point. It has magnitude and direction because
it is a vector.
The distance (D) of an object is the length of the path travelled from the starting point to the
end point. It has magnitude only because it is a scalar.
Displacement is the black line and distance is the blue line.

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Speed and velocity
Speed (v) is the distance covered (D) divided by the time taken (∆t):
Average velocity ( ) is the displacement (∆x) divided by the time taken (∆t):
Instantaneous speed is the speed at a specific instant in time.
Instantaneous velocity is the velocity at a specific instant in time.
⃗vav
v=
D
Δt
⃗vav=
Δ x
Δt

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Acceleration
Acceleration (a) is the change in velocity ( ) over a time interval (∆t):
a=
Δ⃗v
Δt
Δ⃗v

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Graphs of motion
● The gradient of a
position - time graph (x
vs. t) gives the velocity.
● The gradient of a
velocity - time graph (v
vs. t) gives the
acceleration.
● The area under a
velocity - time graph (v
vs. t) gives the
displacement.
● The area under an
acceleration - time graph
(a vs. t) gives the velocity.

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Equations of motion
The equations of motion are used where constant acceleration takes place.
⃗vf =⃗vi +⃗at
Δ⃗x=
(⃗vi + ⃗vf )
2
t
Δ⃗x=⃗vi t+
1
2
⃗at2
⃗vf
2
= ⃗vi
2
+2⃗aΔ⃗x

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