A vector can be broken down into vertical and horizontal components.
Example of vector resolution: a vector can resolve into 2 right (horizontal) and 3 up (vertical).
Resolution of vectors is clearer on graph paper, but can be calculated using the vector's magnitude and direction.
To find components, know the vector's length and the angle to the horizontal or vertical axis.
Once vectors are resolved, their components can be added together.
Process of adding resolved vectors:
Resolve vector C into its components.
Calculate the resultant of the horizontal and vertical components.
Combine these results to find the overall resultant vector.
Find the resultant angle using trigonometry.
Equilibrium occurs when all forces cancel, resulting in no motion or uniform motion.
As an example, the downwards forces (gravity) are balanced by upwards forces (normal force).
In equilibrium, vectors can be visualized as arrows connected head to tail, returning to the starting point indicating a resultant of zero.
Distance:
Scalar quantity, representing total movement length.
Displacement:
Vector quantity, representing how far from starting position.
Example: Completing a 400m lap
Distance = 400m; Displacement = 0m.
Speed:
Measure of distance covered with time, scalar in nature.
Velocity:
Measure of displacement with time, vector in nature.
Both are measured in m/s.
Time: measured in seconds (s).
Acceleration:
Rate of velocity change, also a vector quantity, measured in m/s².
Depends on positive/negative directions:
Positive velocity with positive acceleration = increasing velocity.
Positive velocity with negative acceleration = decreasing velocity.
When acceleration is constant, velocity increases uniformly over time.
Example analysis of uniform acceleration at 2 m/s²:
Velocity (m/s) increases linearly: 0, 2, 4, 6, etc., over Time (s): 0, 1, 2, 3, etc.
Calculated using the change in the y-axis over the change in the x-axis.
Area calculation for straight lines involves:
Rectangles: Area = base × height
Triangles: Area = ½ base × height
Graph A: Displacement constant, object stationary.
Graph B: Constant velocity, displacement increasing linearly.
Graph C: Accelerating, displacement increasing non-linearly.
Graph A: Constant velocity.
Graph B: Uniform acceleration, velocity increasing consistently.
Graph C: Non-uniform acceleration, velocity increases at an increasing rate.
Area under velocity-time graph indicates displacement.
Objects fall freely, accelerating due to gravitational force, irrespective of mass (feather vs. bowling ball).
Near the Earth’s surface:
Gravitational field strength = 9.81 N/kg.
Acceleration of falling objects = 9.81 m/s².
Weight: Force due to gravity, calculated as:
Weight (W) = Mass (m) × Gravitational field strength (g)
Measured in Newtons (N).
Objects accelerate due to weight until drag force equals weight, stopping acceleration at terminal velocity.
Parabolic path dictated by horizontal (u cos θ) and vertical (u sin θ) components of initial velocity.
Horizontal motion: constant velocity.
Vertical motion: acceleration due to gravity (9.81 m/s²).
Horizontal and vertical motions act independently.