Motion

While a falling object is speeding up, weight is still greater than air resistance. The gap between those forces can shrink, so the downward acceleration becomes smaller without becoming negative. A curve that flattens on a speed–time graph shows this gradual reduction in acceleration, not an abrupt disappearance of gravity.

If the object's shape changes, its terminal speed can change too. Immediately after a parachute opens, drag can exceed weight and slow the descent. As the speed falls, drag falls until the forces balance again. Distinguish the short slowing-down stage from the later steady descent, and assume the surrounding conditions remain approximately unchanged.

A graph need not pass through the origin. If a straight segment starts later in a journey, use the differences between two coordinates on that segment. Dividing the final distance coordinate by the final time coordinate can accidentally mix in earlier stages, giving a different average instead of the segment's speed.

Check what the vertical axis actually means. A displacement–time graph gives velocity, which can be negative when the object moves in the chosen negative direction. A graph labelled distance from a fixed point can fall as the object returns, whereas total distance travelled cannot decrease. Interpret the stated quantity before attaching a direction to the gradient.

The area has the right physical units: metres per second multiplied by seconds gives metres. When the speed rises uniformly from zero, the area is a triangle because the object spends most of the interval below its final speed. Using a full rectangle would overestimate how far it travelled.

If a straight segment starts above zero, its area is a trapezium, or equivalently a rectangle plus a triangle. For a curved graph, estimate using narrow strips or the method specified in the question. On a velocity–time graph, keep signed area for displacement but add the magnitudes of the above- and below-axis areas for total distance.

Imagine a trolley moving right while a constant force acts left. Its positive velocity decreases towards zero. If the force continues after it stops, the trolley starts moving left and gains speed, even though the acceleration has not changed. The sign describes direction throughout both parts of the motion.

A velocity–time line can therefore keep the same negative gradient while crossing the axis. Before the crossing, its distance from the axis decreases; afterwards, that distance increases. The distance from zero velocity represents speed. A negative speed is not needed, and saying the trolley decelerates for the entire interval would miss its reversal.

When speed is constant within each of two stages, the arithmetic mean weights those stages equally in time. For equal distances at different speeds, the slower stage lasts longer, so calculate its time separately. The worked example below uses this two-stage situation; it is not a single uniformly accelerating stage.

The endpoint-speed shortcut for a straight speed–time segment comes instead from its trapezium area. It works because speed changes uniformly during that interval. Include stops when finding the average over a complete journey: stopped time contributes to the denominator without adding distance. For several differently shaped stages, adding their areas and times is safer than averaging two selected readings.

Velocity describes how position changes; acceleration describes how velocity changes. A train travelling steadily along a straight track changes position every second while maintaining the same velocity. Its speed–time graph is horizontal above zero, whereas a stationary train has its speed–time graph on the time axis.

Individual forces may still act. The driving force can balance resistance horizontally while support balances weight vertically. An object at constant speed around a bend is different: direction changes, so velocity changes and acceleration is not zero. Include the straight-line condition whenever you use constant speed as evidence of zero acceleration.