IB DP Physics: SL复习笔记2.1.4 Graphs Describing Motion

Motion Graphs

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

Displacement-Time Graph

  • On a displacement-time graph…
    • Slope equals velocity
    • The y-intercept equals the initial displacement
    • A straight(diagonal) line represents a constant velocity
    • A curved line represents an acceleration
    • positive slope represents motion in the positive direction
    • negative slope represents motion in the negative direction
    • zero slope (horizontal line) represents a state of rest
    • The area under the curve is meaningless

2.1.1-Motion-graphs-1Displacement-time graphs displacing difference velocities

Velocity-Time Graph

  • On a velocity-time graph…
    • Slope equals acceleration
    • The y-intercept equals the initial velocity
    • straight line represents uniform acceleration
    • curved line represents non-uniform acceleration
    • positive slope represents an increase in velocity in the positive direction
    • negative slope represents an increase in velocity in the negative direction
    • zero slope (horizontal line) represents motion with constant velocity
    • The area under the curve equals the change in displacement

2.1.1-Motion-graphs-2Velocity-time graphs displacing different acceleration

Acceleration-Time Graph

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


How displacement, velocity and acceleration graphs relate to each other

Worked Example

Tora is training for a cycling tournament.

The velocity-time graph below shows her motion as she cycles along a flat, straight road.


(a) In which section (A, B, C, D, or E) of the velocity-time graph is Tora’s acceleration the largest?(b) Calculate Tora’s acceleration between 5 and 10 seconds.

Part (a)

Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration

      • The slope of a velocity-time graph indicates the magnitude of accelerationTherefore, the only sections of the graph where Tora is accelerating is section B and section D
      • Sections A, C, and E are flat – in other words, Tora is moving at a constant velocity (i.e. not accelerating)

Step 2: Identify the section with the steepest slope

      • Section D of the graph has the steepest slope
      • Hence, the largest acceleration is shown in section D

Part (b)

Step 1: Recall that the gradient of a velocity-time graph gives the acceleration

      • Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

      • A gradient triangle is drawn for the time period between 5 and 10 seconds below:


Step 3: Calculate the size of the gradient and state this as the acceleration

      • The acceleration is given by the gradient, which can be calculated using:

acceleration = gradient = 5 ÷ 5 = 1 m/s2

      • Therefore, Tora accelerated at 1 m/s2 between 5 and 10 seconds

Motion of a Bouncing Ball

  • For a bouncing ball, the acceleration due to gravity is always in the same direction (in a uniform gravitational field such as the Earth's surface)
    • This is assuming there are no other forces on the ball, such as air resistance
  • Since the ball changes its direction when it reaches its highest and lowest point, the direction of the velocity will change at these points
  • The vector nature of velocity means the ball will sometimes have a:
    • Positive velocity if it is traveling in the positive direction
    • Negative velocity if it is traveling in the negative direction
  • An example could be a ball bouncing from the ground back upwards and back down again
    • The positive direction is taken as upwards
    • This will be either stated in the question or can be chosen, as long as the direction is consistent throughout
  • Ignoring the effect of air resistance, the ball will reach the same height every time before bouncing from the ground again
  • When the ball is traveling upwards, it has a positive velocity which slowly decreases (decelerates) until it reaches its highest point


  • At point (the highest point):
    • The ball is at its maximum displacement
    • The ball momentarily has zero velocity
    • The velocity changes from positive to negative as the ball changes direction
    • The accelerationg, is still constant and directed vertically downwards
  • At point (the lowest point):
    • The ball is at its minimum displacement (on the ground)
    • Its velocity changes instantaneously from negative to positive, but its speed (magnitude) remains the same
    • The change in direction causes a momentary acceleration (since acceleration = change in velocity / time)

Worked Example

The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.v-t-Area-Worked-Example-1Calculate the displacement of the vehicle at 40 s.