physics - kinematics

• Kinematics refers to the bunch of mechanics in physics that is concerned with the motion of a body, or a system of bodies, without consideration of its mass or the forces which cause the motion
• Distance is the total length travelled by the body regardless of the direction of motion.
• Distance is a scaler quantity; the direction of travel does not matter, only the magnitude does.
• The S.I. unit of distance is metre (m).
• Displacement is the distance measured in a straight line in a specified direction.
• Displacement is a vector quantity; meaning that both magnitude and direction needs to be stated.
• The S.I. unit of displacement is metre (m).
• Speed of a body is defined as the distance traveled per unit time.
• Speed = distance traveled / time taken
• Speed is a scaler quantity.
• The S.I. unit of speed is metre per second ($ms^-1$)
• Average speed = total distance traveled / total time taken
• Instantaneous speed is defined as the speed of the body at any given point in time.
• In order to fully describe the motion of a body, we need to describe both the speed and direction of the body, using velocity.
• Velocity = change in displacement / time taken

  (change can be represented with a triangle, a delta sign)
• The symbol for displacement (in equations) is s
• Average velocity = total displacement / total time taken
• Acceleration is defined as the rate of change of velocity or the change in velocity per unit time.
• Acceleration = change in velocity / time taken
• Acceleration is a vector quantity.
• S. I. unit for acceleration is metre per second square (m s-2)
• Rectilinear motion is when a body moves in a straight line or parallel to one. The body moves in one-dimension and can only move in two possible directions, with one direction being the opposite of the other.
• When vector quantities are involved in a question, we have to assign one direction as positive and the other as negative.
• Graphs are used in Physics to give a visual representation of relationships between different physical quantities.
• In kinematics, graphs can be used to show how displacement, velocity and acceleration of a body change with time
• The gradient of a displacement-time graph gives the velocity of the body
• If the gradient of the displacement-time graph is a constant value (a straight line), the velocity of the body is constant (no acceleration). It moves with uniform velocity or is at rest.
• If the gradient of the displacement-time graph is not a constant value (eg, a curved line), the velocity of the body is not constant (non-uniform)
• On a displacement-time graph, a gentle to steep slope reflects increasing velocity while a steep to gentle slope indicates a decreasing velocity.

  Increasing gradient = increasing magnitude of velocity

  Decreasing gradient = decreasing magnitude of velocity

  
• When a displacement-time graph has a positive gradient, the body is moving in a positive direction and has positive velocity.
• When a displacement-time graph has a negative gradient, the body is moving in the negative direction and has a negative velocity.
• For all graphs, the gradient of a curve can be described in two parts:

  1. Sign of the gradient of the curve (positive, negative or zero)
  2. Changes to the magnitude of the gradient (increasing, decreasing or constant)
• The gradient of the velocity - time graph is the change in velocity over the change in time, the same as acceleration
• The gradient of the velocity - time graph is the acceleration
• The area under velocity - time graphs is the change in displacement
• A body moving with constant acceleration will be reflected with a straight line (constant gradient) on a velocity - time graph as the body moves proportionally with time.
• Non-uniform acceleration, also known as terminal velocity is reflected with a curve on the velocity - time graph.
• If the change in velocity occurs at an increasing rate, the object is said to be experiencing increasing acceleration.

  On a velocity - time graph, it will be reflected as

  
• If the change in velocity occurs at an decreasing rate, the object is said to be experiencing decreasing acceleration.

  On a velocity - time graph, it will be reflected as

  
• A velocity - time graph with a 0 gradient indicates that an object is at rest (line is on the x axis, y=0) or moving at a constant velocity (ie, no acceleration or deceleration)