Higher Physics - Dynamic Universe (Vectors, Equations of Motion, Graphs of Motion)

Scalar Quantity Definition

Scalar Quantity Definition

Scalars only have magnitude

Scalar Quantity Examples

• Distance

• Speed

• Time

• Energy

Vector Quantity Definition

Vectors have both direction and magnitude

Adding Vectors (Right Angled)

Nose to tail, find magnitude using Pythagoras (a² = b² + c²), must also find direction using Trigonometry (tan θ = Opposite/Adjacent) to get full marks

Adding Vectors (Non-Right Angled)

Nose to tail, find magnitude using Cosine Rule (a²=b²+c²-2bc cos A) where:

• a = Resultant Vector

• b = First Vector

• c = Second Vector

• A = Bearing angle given

Then find direction of resultant using Sine Rule (a/sinA = b/sinB) where:

• a = First Vector

• b = Second Vector

• A = Angle between vectors

• B = Resultant direction angle

Seperating Vectors Into Components (Horizontal Component)

Cos = Across

(Horizontal Component = a cos θ) where:

• a = Resultant Vector

• θ = Direction of Vector

Seperating Vectors Into Components (Vertical Component)

Sine = Climb

(Vertical Component = a cos θ) where:

• a = Resultant Vector

• θ = Direction of Vector

Equations of Motion

v = u + at

s = ut + ½ at²

v² = u² + 2as

s = (u + v)/(2) t

Where:

• s = Displacement

• u = Initial Velocity

• v = Final Velocity

• a = acceleration

• t = time

Velocity-Time Graph

Shows how the velocity of a moving object changes with time, where:

• Increasing Gradient = Constant Acceleration

• Flat Line = Constant Velocity

• Decreasing Gradient = Constant Deceleration

Note - Flat Line on x-axis (time axis) = At Rest (Zero Velocity)

Calculating Acceleration using V-T Graph

Acceleration can be calculated through

• Acceleration = gradient of graph

Note - Negative Gradient = Deceleration

Calculating Displacement Using V-T Graph

Displacement can be calculated through

• Displacement = area of graph

Note - Area made up of separate shapes must be split up