P1 | Motion, Forces & Energy

• • All quantities can be one of two types:
  • A scalar
  • A vector
• Scalars

  • Scalars are quantities that have only a magnitude
  • For example, mass is a scalar since it is a quantity that has magnitude without a direction
  • Distance is also a scalar since it only contains a magnitude, not a direction
• Vectors

  • Vectors have both magnitude and direction
  • Velocity, for instance, is a vector since it is described with both a magnitude and a direction
  • When describing the velocity of a car it is necessary to mention both its speed and the direction in which it is travelling
  • For example, the velocity might be 60 km per hour (magnitude) due west (direction)
• • Distance is a value describing only how long an object is or how far it is between two points - this means it is a scalar quantity
• • Displacement describes the direction in which the distance is measured - this means it is a vector quantity
  • For example, a displacement might be 100 km north
• • Some vectors and scalars are similar to each other
  • For example, the scalar quantity distance corresponds to the vector quantity displacement
• • Vectors are represented by an arrow
  • The arrowhead indicates the direction of the vector
  • The length of the arrow represents the magnitude

  A) Magnitude

  B) Direction

  C) Magnitude

  D) Direction

  
• • The speed of an object is the distance it travels per unit time
• Speed is a scalar quantity
• For objects that are moving with a constant speed, use the equation below to calculate the speed:

  speed = distance travelled / time taken
• Speed is measured in metres per second
• Distance travelled is measured in metres
• Time taken is measured in seconds
• The equation for calculating the average speed of an object is:

  average speed = distance travelled / time taken
• The velocity of a moving object is similar to its speed, except it also describes the object’s direction
• Velocity is therefore a vector quantity because it describes both magnitude and direction
• Velocity can also have a negative value
• • Velocity is a vector quantity, so it uses displacement, s, rather than distance which is scalar. 
• Acceleration is defined as the rate of change of velocity
•  Acceleration describes how much an object's velocity changes every second
• change in velocity = final velocity − initial velocity
• An object that speeds up is accelerating
• An object that slows down is decelerating
• The acceleration of an object can be positive or negative, depending on whether the object is speeding up or slowing down
• If an object is speeding up, its acceleration is positive
• If an object is slowing down, its acceleration is negative
• A speed-time graph shows how the speed of a moving object varies with time
• If there is a change in an object's speed, then it is accelerating
• An object may accelerate at a steady rate, this is called constant acceleration
• The acceleration of an object can be calculated from the gradient of a speed-time graph
• In the absence of air resistance, all objects fall with the same acceleration
• Mass is a measure of the quantity of matter in an object at rest relative to the observer
• The weight of two objects can be compared using a balance
• Density is defined as:

  The mass per unit volume of a material
• Objects made from low density materials typically have a low mass
• Similarly sized objects made from high density materials have a high mass
• Density is related to mass and volume by the following equation: density = mass / volume
• Gases are less dense than solids because the molecules are more spread out 
• Gravitational field strength is defined as:

  The force per unit mass acting on an object in a gravitational field
• On Earth, Gravitational field strength is equal to 9.8 N/kg