Motion Graphs in Aerospace Engineering

Motion Graphs

• Motion graphs are covered in Aerospace Engineering Topic 1: Motion

Knowledge Checklist: Motion Graphs

• Distance-time graphs
• Displacement-time graphs
• Speed-time graphs
• Velocity-time graphs
• Significance of the gradients of, and areas under the various graphs

Note-Taking Guide Solutions

• The gradient of a distance-time graph represents speed.
• The area under a distance-time graph represents N/A.
• The gradient of a displacement-time graph represents velocity.
• The area under a displacement-time graph represents N/A.
• The gradient of a speed-time graph represents the magnitude of acceleration (no direction).
• The area under a speed-time graph represents the distance.
• The gradient of a velocity-time graph represents acceleration.
• The area under a velocity-time graph represents displacement.

Comparison: Distance-Time Graphs and Displacement-Time Graphs

• Distance-time graphs do not specify a direction on the y-axis.
• In distance-time graphs, values cannot be negative because distance cannot be negative.
• Distance-time graphs cannot go downwards because distance does not decrease.
• In distance-time graphs, a zero gradient means the object is still.
• Displacement-time graphs specify a direction on the y-axis.
• Displacement-time graphs can have negative values, indicating the direction is behind the starting point.
• Displacement-time graphs can go downwards, indicating a return towards the starting point.
• In displacement-time graphs, a zero gradient means the object is still.

Example 1: Distance-Time and Displacement-Time Graphs

• Erin has embarked on a short trip.
• Erin was West of her starting point from 0s - 6.25s
• Erin was East of her starting point from 6.25s - 7.5s
• Erin was moving West from 0 s 2s
• Erin was moving East from 5s - 7.5s
• Erin was stationary from 2s - 5s

Velocity-Time Graphs

• Velocity-time graphs can easily fool students because they are not a picture of the object's path.
• Use common sense, but avoid intuition.
• Make a story in your head and draw a diagram of what is happening.

Example 2: Velocity-Time Graphs

• A data recorder was attached to a small working model of a space rocket during a test launch.
• The 7.0 kg rocket's vertical velocity was recorded at various points in time.
• The graph shows the data until just before the rocket reaches ground level.
• The model rocket started to take off from the ground at t = 3s
• The rocket ran out of fuel for its engine at t = 5s (when it stopped speeding up and began to slow down)
• The model rocket reached the highest point of its test flight at t = 9s (when it stopped moving upwards and started moving downwards)
• At t = 4s, the rocket's velocity was 10 m/s upwards

Example 3: Velocity-Time Graphs

• Katie is on a short jog.
• Katie was moving East, during the time interval from 0.0s - 24.0s.
• Katie's acceleration between 0.0s and 16.0s was 0 m/s/s.
• Katie was stationary at t = 24.0s

Comparison: Speed-Time Graphs and Velocity-Time Graphs

• Speed-time graphs do not specify a direction on the y-axis.
• Speed-time graphs cannot be negative because speed cannot be negative.
• Speed-time graphs can go downwards because speed can decrease.
• A 0 gradient indicates the object is moving at a constant speed in speed-time graphs.
• Velocity-time graphs should specify a direction on the y-axis.
• Velocity-time graphs can have negative values, indicating movement in the opposite direction.
• Velocity-time graphs can go downwards because velocity can decrease.
• A 0 gradient means the object moves at a constant velocity in velocity-time graphs.