Scalar quantities

• Scalar quantities only have a magnitude (size)
  • Distance:?the total length between two points
  • Speed:?the total distance travelled per unit of time

   

Vector quantities

• Vector quantities have both magnitude and direction
  • Displacement:?the distance of an object from a fixed point in a specified direction
  • Velocity:?the rate of change of displacement of an object
  • Acceleration:?the rate of change of velocity of an object

   

Equations for Velocity & Acceleration

Equations linking displacement, velocity and acceleration

Instantaneous Speed / Velocity

• The instantaneous speed (or velocity) is the speed (or velocity) of an object at any given point in time
• This could be for an object moving at a constant velocity or accelerating
  • An object accelerating is shown by a?curved line?on a displacement – time graph
  • An accelerating object will have a changing velocity

   

• To find the instantaneous velocity on a displacement-time graph:
  • Draw a?tangent?at the required time
  • Calculate the?gradient?of that tangent

   

The instantaneous velocity is found by drawing a tangent on the displacement time graph

Average Speed / Velocity

• The average speed (or velocity) is the?total distance?(or displacement) divided by the?total time
• To find the average velocity on a displacement-time graph, divide the?total displacement?(on the y-axis) by the?total time?(on the x-axis)
  • This method can be used for both a curved or a straight-line on a displacement-time graph

   

Step 1: Write the average speed equation

Average speed = total distance ÷ total time

Step 2: Calculate the total distance

Total distance = 20 + 5 = 25 m

Step 3: Calculate the average speed

Average speed = 25 ÷ 3.5? = 7.1 m s-1

• Three types of graph that can represent motion are displacement-time graphs, velocity-time graphs and acceleration-time graphs

Displacement-Time Graph

• On a?displacement-time graph:
  • The?gradient?(or slope)?equals?velocity
  • The?y-intercept?equals the?initial displacement
  • A diagonal?straight?line represents a?constant?velocity
    • A?positive?slope?represents motion in the?positive?direction
    • A?negative?slope?represents motion in the?negative?direction

     

  • A?curved?line represents an?acceleration
  • A?horizontal line?(zero slope) represents a state of?rest
  • The area under the curve is meaningless

   

• Remember the displacement-time graph can have positive or negative values on the displacement axis. However, a distance-time graph only has positive

Displacement-time graph for different scenarios

Velocity-Time Graph

• On a?velocity-time graph:
  • Slope?equals?acceleration
  • The?y-intercept?equals the?initial velocity
  • A?straight?line represents?uniform?acceleration
    • A?positive?slope represents an?increase?in?velocity?(acceleration) in the?positive?direction
    • A?negative?slope represents an?increase?in?velocity?(acceleration) in the?negative?direction

     

  • A?curved?line represents the?non-uniform acceleration
  • A?horizontal?line (zero slope)?represents motion with?constant?velocity
  • The?area?under the curve equals the?displacement?or?distance?travelled

   

• Remember the velocity-time graph can have positive or negative values on the displacement axis. However, a speed-time graph only has positive

Velocity-time graph for different scenarios

Acceleration-Time Graph

• On an?acceleration-time graph:
  • The slope is meaningless
  • The?y-intercept?equals the?initial acceleration
  • A horizontal line (zero slope) represents an object undergoing?constant acceleration
  • The?area?under the curve equals the?change in velocity

   

Acceleration-time graphs for different velocity scenarios