Drawing Travel Graphs (AQA A-Level Mathematics): Revision Notes

• Axes:
• Time ($t$) is plotted on the horizontal axis ($x$-axis).
• Displacement ($s$) is plotted on the vertical axis ($y$-axis).
• Displacement:
• Displacement is the distance from a reference point (often the origin) in a specific direction.
• Types of Motion Represented:
• Uniform motion (constant velocity).
• Accelerated or decelerated motion (changing velocity).
• Stationary (no change in displacement).

1. Identify Key Points:

• Determine the starting position (initial displacement).
• Identify any changes in speed, direction, or when the object is stationary.

2. Plotting the Graph:

• Start from the Initial Displacement: Begin by plotting the initial displacement at $t = 0$ .
• Draw the Line Segments: Depending on the motion, connect the points with straight or curved lines.
• Label Important Points: Mark where the object changes speed or direction, stops, or turns around.

3. Different Scenarios:

• Constant Velocity:
• Draw a straight line with a constant slope.
• A positive slope indicates motion in the positive direction.
• A negative slope indicates motion in the opposite direction.
• Acceleration:
• Draw a curve that becomes steeper over time.
• Indicates increasing speed.
• Deceleration:
• Draw a curve that flattens out over time.
• Indicates decreasing speed.
• Stationary Object:
• Draw a horizontal line, indicating no change in displacement.

4. Check the Gradient:

• The gradient (slope) of the graph represents the velocity of the object.
• Ensure the graph's gradient matches the given or expected velocity at different intervals.

Example : 5. Uniform Motion:

• An object moves with a constant velocity of $4$ $m/s$ for $5$ $seconds$.
• Graph: Draw a straight line starting from the origin $(0,0)$ to $(5, 20)$, where $s = 20$ $metres$ (calculated as velocity × time).

6. Acceleration:

• An object starts from rest and accelerates uniformly over $4$ $seconds$.
• Graph: Start at the origin. The curve should start shallow and get steeper as time progresses, indicating increasing displacement.

7. Deceleration:

• An object is moving at $10$ $m/s$ and slows down uniformly to stop in $5$ $seconds$.
• Graph: Start from the initial displacement (e.g., at $s = 50$ $metres$ if it's decelerating from $10$ $m/s$ over $5$ $seconds$) and draw a curve that flattens out as the object comes to a stop.

8. Changing Direction:

• An object moves $10$ $metres$ in the positive direction, stops for $2$ $seconds$, and then returns to the starting point.
• Graph: Draw a straight line from the origin to $(5, 10)$, then a horizontal line (showing the stop), followed by a line with a negative slope back to the origin.

• Area Under the Graph:
• The area under a displacement-time graph doesn't have a physical meaning like it does in velocity-time graphs, but the shape and gradient give insight into the motion.
• Zero Slope:
• A zero slope (horizontal line) indicates the object is stationary.
• Crossing the Time Axis:
• If the graph crosses the time axis (where displacement is zero), it indicates that the object has returned to its starting point.

• Incorrect Scaling: Ensure that both time and displacement axes are correctly scaled to accurately represent the motion.
• Mismatched Slopes: The slope must correctly reflect the given velocities. A steeper slope for higher velocity, and a flatter slope for lower velocity or stationary motion.

Drawing travel graphs in A-Level Mechanics involves understanding the relationship between time and displacement, plotting key motion events, and correctly interpreting the slope of the graph. Practice with different scenarios—uniform motion, acceleration, deceleration, and changes in direction—will build your ability to accurately draw and analyse these graphs.