Velocity-Time Graph

• What do distance-time graphs show?


  How the distance of an object varies over time
• What do velocity-time graphs show?


  How an object's velocity changes over time
• Why is it easy to confuse distance-time graphs with velocity-time graphs?


  Because they look pretty similar
• What is plotted on the y-axis of a velocity-time graph?

  Velocity
• What is plotted on the x-axis of a velocity-time graph?

  Time
• How do you find the gradient of the curve on a velocity-time graph?

  By calculating the change in velocity over the change in time
• What does the gradient of a velocity-time graph represent?

  The acceleration of the object
• What does a constant positive gradient on a velocity-time graph indicate?

  The object is experiencing a constant acceleration
• What does a constant negative gradient on a velocity-time graph indicate?

  The object is experiencing constant deceleration
• How do you calculate acceleration from a velocity-time graph?

  By dividing the change in velocity by the change in time
• If the change in velocity is 3 m/s and the change in time is 2 s, what is the acceleration?

  $1.5 \text{ m/s}^2$
• What does a flat section of the curve on a velocity-time graph indicate?

  The object is moving at a constant velocity
• How do you find the velocity during flat sections of a velocity-time graph?

  By looking at the y-axis
• What is the velocity during the second stage if it is 3 m/s?

  3 m/s
• What is the velocity during the fourth stage if it is 5 m/s?

  5 m/s
• What does a steeper curve in a velocity-time graph indicate?

  The rate of acceleration is increasing
• How do you find the distance traveled from a velocity-time graph?

  By calculating the area under the curve
• How can you simplify the calculation of the area under the curve?

  By splitting the area into shapes like triangles and rectangles
• What is the formula for the area of a triangle?

  Area = \frac{1}{2} \times \text{base} \times \text{height}
• What is the area of a triangle with a base of 2 seconds and a height of 3 m/s?

  $3 \text{ m}$
• How do you calculate the area of a rectangle?

  By multiplying the base by the height
• What is the area of a rectangle with a base of 2 seconds and a height of 3 m/s?

  $6 \text{ m}$
• What is the total distance traveled during the first four seconds if the areas are 3 m and 6 m?

  $9 \text{ m}$
• Why is the area under the curve given in meters instead of meters squared?

  Because we are finding the distance traveled
• How can you estimate the area under curved parts of the graph?

  By counting the number of squares under that section of the graph
• If each square in the grid equals one meter of distance, how many squares are under the curved section if there are six full squares and two partial squares?

  Approximately eight squares
• What is the total distance traveled over the two seconds if the area under the curve is approximately eight squares?

  Approximately eight meters
• What are the key differences between distance-time graphs and velocity-time graphs?


  • Distance-time graphs show distance vs. time.
  • Velocity-time graphs show velocity vs. time.
  • Distance-time graphs have distance on the y-axis.
  • Velocity-time graphs have velocity on the y-axis.
• What are the steps to calculate the area under a velocity-time graph?

  1. Identify the shapes formed under the curve (triangles, rectangles).
  2. Calculate the area of each shape using appropriate formulas.
  3. Sum the areas to find the total distance traveled.