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

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Physics

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11 Terms

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Scalar Quantity Definition

Scalars only have magnitude

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Scalar Quantity Examples

  • Distance

  • Speed

  • Time

  • Energy

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Vector Quantity Definition

Vectors have both direction and magnitude

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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

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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

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Seperating Vectors Into Components (Horizontal Component)

Cos = Across

(Horizontal Component = a cos θ) where:

  • a = Resultant Vector

  • θ = Direction of Vector

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Seperating Vectors Into Components (Vertical Component)

Sine = Climb

(Vertical Component = a cos θ) where:

  • a = Resultant Vector

  • θ = Direction of Vector

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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

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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)

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Calculating Acceleration using V-T Graph

Acceleration can be calculated through

  • Acceleration = gradient of graph

Note - Negative Gradient = Deceleration

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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