First, remember that 'acceleration' is any change in the object's speed*** or ***direction. So the object is accelerating if it's speeding up, or slowing down, or moving in a curve.
If it's speeding up or slowing down, then the graph of its speed vs. time is anything different from a horizontal line.
If it's moving in a curve but maintaining a constant speed, then the speed vs. time graph doesn't reveal it, although the object is technically still accelerating.
To determine acceleration on a speed vs. time graph, observe the slope: a positive, negative, or changing slope indicates acceleration, deceleration, or changing acceleration, respectively. A flat horizontal line suggests zero acceleration. On a distance vs. time graph, a straight line indicates constant velocity and a steeper slope implies faster velocity.
To determine if an object is accelerating by looking at a speed vs. time graph, you need to observe the slope of the graph. If the speed increases over time, the slope of the graph will be positive, indicating acceleration. Conversely, if the speed decreases, the graph will slope downwards, indicating deceleration. A constant slope indicates a constant acceleration. However, if the slope is changing - the line curves on the graph - that indicates changing acceleration. Specifically, if the slope becomes steeper, the object accelerates faster, and if it flattens out, the acceleration decreases. Moreover, if the velocity line is horizontal (no slope), it indicates that the object is moving at a constant speed and thus has zero acceleration.
As for a Distance vs. Time graph, if the velocity is constant, the graph will be a straight line, indicating a steady increase in distance over time. If a car has a faster velocity, its distance vs. time graph would have a steeper slope compared to a car moving slower.
To determine if an object is accelerating from a speed vs. time graph, check if the graph is a horizontal line or varies in slope. A horizontal line indicates no acceleration, while any changing slope indicates acceleration. Curved lines also suggest changes in acceleration rates, even if speed appears constant in some cases.
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