velocity-time graphs

• 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 both graphs look 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
• 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 with 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 constant at 3 m/s?


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


  5 m/s
• What does a steeper gradient 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 calculate the area under the curve for the first four seconds?


  By splitting it into a triangle and a rectangle
• What is the area of the triangle formed in the first section if the base is 2 seconds and the height is 3 m/s?


  $3 \text{ m}$
• What is the area of the rectangle formed in the first section if the base is 2 seconds and the height is 3 m/s?


  $6 \text{ m}$
• What is the total distance traveled during the first four seconds?


  $9 \text{ m}$
• 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 traveled, how many squares are there in the curved section if there are six full squares and two partial squares?


  Almost eight squares
• What is the total distance traveled over the two seconds in the curved section if it is almost 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 sections (triangles, rectangles)
  2. Calculate area for each section:

  • Triangle: \( \frac{1}{2} \times \text{base} \times \text{height} \)
  • Rectangle: \( \text{base} \times \text{height} \)

  1. Sum the areas for total distance