Graphs of Motion

The gradient on a displacement-time graph represents the velocity. This is due to velocity = change in displacement/change in time. When the line is linear, it means that the velocity is constant. The steeper the gradient, the faster the constant velocity is. If the linear line is horizontal, it means that there is no change in the displacement and therefore the velocity is 0. If there is a curved line in the displacement-time graph, then it means that there is either acceleration or deceleration. If the curve gets steeper as time progresses, then it is accelerating. If the curve gets shallower as time progresses, then the object is decelerating. The area underneath the curve does not represent anything. The gradient on a velocity-time graph represents the acceleration. This is due to acceleration = change in velocity/ change in time. If the linear line has a positive gradient, then the object is uniformly accelerating. If the linear line has a negative gradient, then the object is uniformly decelerating. If the linear line has a gradient of 0, then the object is not accelerating and has a constant velocity. If there is a curved line in the velocity-time graph, then the object has an increasing velocity. The area underneath a velocity-time graph represents the displacement of the object. This is due to velocity = change in displacement/change in time. Therefore, velocity x time is the change in displacement = area under the line/curve.



The area underneath an acceleration-time graph represents the velocity of the object. This is due to acceleration = change in velocity/change in time. Therefore, acceleration x time = velocity = area under the line. The gradient of the line does not represent anything.