Displacement-Time Graphs

• Straight Lines: A straight diagonal line indicates that the gradient is constant, which means the object is moving at a constant velocity.

• Curved Lines: A curve indicates a changing gradient, which implies the object is either accelerating or decelerating.

• Increasing Steepness: If a curve becomes steeper over time, the velocity is increasing, indicating acceleration away from the current direction.

• Decreasing Steepness: If a curve levels off toward a horizontal slope, the velocity is decreasing, indicating deceleration.

Displacement vs. Distance

• Displacement is the vector difference between the final and initial positions; it can be negative if the object moves behind the origin.
• Distance is the total path length traveled and is always a non-negative scalar quantity.

Average Velocity vs. Average Speed

• Check the Y-Axis: Always verify if the graph is displacement-time or velocity-time, as the meaning of the gradient and area changes entirely between them.

• Identify the Origin: Look at where the graph starts on the y-axis; an object starting at $s = 50$ is already 50 units away from the origin at $t = 0$.

• Sign Consistency: Ensure that 'forwards' and 'backwards' motion are consistently assigned positive and negative gradients respectively.

• Units Check: Always include units in your final calculations (e.g., $m s^{-1}$ for velocity) and ensure they match the axes labels.

• Area Misinterpretation: A common error is attempting to calculate the area under a displacement-time graph; unlike velocity-time graphs, this area has no standard physical significance in basic kinematics.

• Confusing Speed with Velocity: Students often forget that a negative gradient represents a positive speed in the opposite direction, not a 'negative speed'.

• Stationary vs. Origin: Touching the x-axis means the object is at the origin, but it does not necessarily mean it is stationary; it could be passing through the origin at high speed.