Displacement-Time Graphs

Horizontal Line: A gradient of zero means the velocity is zero, indicating the object is stationary at a specific displacement from the origin.

Straight Diagonal Line: A constant gradient indicates that the object is moving with a constant velocity (no acceleration).

Curved Line: A changing gradient indicates that the velocity is changing over time, meaning the object is accelerating or decelerating.

Crossing the T-axis: When the line crosses the horizontal axis, the displacement is zero, meaning the object is exactly at the reference origin.

To calculate constant velocity from a straight-line segment, use the gradient formula: $v = \frac{\Delta s}{\Delta t} = \frac{s_2 - s_1}{t_2 - t_1}$.

For average velocity over a total journey, divide the total displacement (final position minus initial position) by the total time taken: $v_{avg} = \frac{s_{final} - s_{initial}}{t_{total}}$.

To find average speed, calculate the total distance travelled (the sum of the absolute lengths of all movements) and divide by the total time: $speed_{avg} = \frac{Total\ Distance}{Total\ Time}$.

For curved graphs, the instantaneous velocity at a specific time is found by drawing a tangent to the curve at that point and calculating its gradient.

Check the Units: Always verify the units on both axes (e.g., meters and seconds vs. kilometers and hours) before performing calculations to ensure the velocity units are correct.

Sign Matters: In mechanics problems, a negative velocity is just as important as a positive one; it indicates direction. Never ignore a downward slope.

Identify Segments: Break complex graphs into distinct segments (stationary, constant velocity, accelerating) before attempting to describe the overall motion.

Sanity Check: If a graph shows a vertical line, it implies infinite velocity (moving through space in zero time), which is physically impossible and usually indicates an error in drawing or interpretation.