Motion

By Nico Vaunois - 2011

Distance and Displacement

Distance is the measure of the total length of the path taken during the change of position of an object

Distance is a scalar quantity

Displacement is the measure of the change of position of an object

Displacement is a vector quantity

Speed and Velocity

Speed is the measure of rate of the distance covered

Speed is a scalar quantity

Velocity is the measure of rate of displacement of an object

Velocity is a vector quantity

Speed (m/s) =

Distance covered (m)Time taken (s)

Velocity =

Displacement

Time taken

Scalars and Vectors

Scalars are quantities that have a size (or magnitude) only

Vectors are quantities that have a size and a direction

Speed Distance Time

We can calculate the speed of a moving object using the equation :

Average Speed =

Distance covered

Time taken

Because distance is measured in metres (m) and time in seconds (s), the S.I. unit for speed is metres per second (m/s or m s-1)

Speed (m/s) =

Distance covered (m)Time taken (s)

s =

d

t

ds t

Acceleration

Acceleration is the rate of change of speed

Acceleration = Change in VelocityChange in Time

Because speed is measured in metres per second (m s-1) and time in seconds (s), the S.I. unit for acceleration is :

metres per second squared (m/s/s or m s-2)

Acceleration (m s-

2) =

Change in velocity (m s-1)Change in

time (s)

a =

Δv

Δt

Δva Δt

Time (s)

Distance (m) Distance (m)

Time (s)

Speed (m/s)

Time (s)

Speed (m/s)

Time (s) Time (s)

Speed (m/s) Speed (m/s)

Time (s)

Distance (m)

Time (s)

Distance (m)

Time (s)

Distance – Time graphSpeed – Time graph

Distance (m)

Time (s)

On a distance time graph, the slope or gradient of the line represents the speed of the object at the time

Steeper slope Greater gradient Greater speed No slope gradient = 0 No speed No movement Curved line change in gradient change in speed

Distance – Time graph

Speed (m/s)

Time (s)

Speed – Time graph

On a speed time graph, the slope or gradient of the line represents the acceleration of the object at the time

No slope gradient = 0 No acceleration Constant speed Steeper slope Greater gradient Greater acceleration

On a speed time graph, the area under the graph represents the distance covered

Velocity - time graphs

• Distance and displacement can be found from a velocity - time graph by

time

velo

city

+

-

Area 1

Area 2

Area 1 + Area 2 = Distance Area 1 – Area 2 = Displacement

Distance (m)

Time (s)

Speed (m/s)

Time (s)

Distance – Time graphSpeed – Time graph

Speed Distance Time

We can calculate the speed of a moving object using the equation :

Average Speed =

Distance coveredTime taken

Because distance is measured in meters (m) and time in seconds (s), the S.I. unit for speed is meters per second (m/s or m s-1)

Speed (m/s) =

Distance covered (m)Time taken (s)

s =

d

t

ds t

Acceleration

Acceleration is the rate of change of speed

Acceleration = Change in SpeedChange in Time

Because speed is measured in meters per second (m s-1) and time in seconds (s), the S.I. unit for acceleration is :

meters per second squared (m s-1 /s or m s-2)

Acceleration (m s-

2) =

Change in speed (m s-1)Change in time (s)

a =

Δv

Δt

Δva Δt