Higher Physics SQA

Motion - Equations and Graphs

Motion - Equations and Graphs

Understanding Distance-Time Graphs

• Distance-Time Graphs depict how an object's distance varies with time.
• The gradient represents speed. A steeper gradient equates to a faster speed.
• A horizontal line signifies that the object is stationary.
• Curved lines signify that the object's speed is changing.
• The area under the graph is not generally significant in a distance-time graph.

Interpreting Velocity-Time Graphs

• Velocity-Time Graphs indicate how velocity varies over time.
• The gradient of the graph represents acceleration. A steeper gradient abrogates a larger acceleration.
• A horizontal line on a Velocity-Time Graph denotes uniform (constant) velocity.
• A line of an increasing gradient indicates increasing speed, meaning the object is speeding up.
• A line of decreasing gradient indicates reducing speed, meaning the object is slowing down.
• The area under the graph depicts distance travelled.

Speed, Velocity, and Acceleration: Key Equations

• The average speed of an object is given by the total distance travelled divided by the total time taken (

  speed = distance / time

  ).
• Velocity is defined as speed in a given direction.
• Acceleration (

  a

  ) can be calculated using the formula

  a = (v - u) / t

  , where

  v

  is final velocity,

  u

  is initial velocity, and

  t

  is time.
• The SUVAT equations are a set of five equations used to solve motion problems, including

  s = ut + 0.5at^2

  , where

  s

  is displacement,

  u

  is initial velocity,

  a

  is acceleration, and

  t

  is time.

Newton's Laws of Motion

• Newton's First Law states that an object will stay at rest or continue to move at constant velocity unless acted upon by an unbalanced force.
• Newton's Second Law establishes that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (

  Force = mass x acceleration

  ).
• Newton’s Third Law avers that for every action, there is an equal and opposite reaction.

Circular Motion

• In circular motion, an object moves in a circular path due to a central force, often gravity.
• Centripetal force is the force that keeps an object moving in a circle and always acts towards the centre of the circle.
• The equation for centripetal force is

  F = mv^2 / r

  , where

  m

  is mass,

  v

  is velocity, and

  r

  is the radius of the circle.
• The centripetal acceleration always points toward the centre of the circle and can be calculated by

  a = v^2 / r

  .