Displacement is the area under the v-t graph.
An x-t graph shows displacement over time, and a v-t graph shows velocity over time. The combination of the two graphs can give you great detail about the motion of an object over a given period of time. For example, if an object moved 2 cm over 2 seconds on the x-t graph, that says nothing about what direction the object moved in, but if you combine that data with the v-t graph and see that over those 2 seconds the object had a positive acceleration, that means that the object was moving away from the origin of the graph.
The distance travelled over the time period represented by the area under the v-t graph between the end points.
If an x-t graph is a position-time graph, velocity is the slope of the line on the graph.
v = a t a = v / t Bonus: t = v / a
The uses of the V-T graph include finding acceleration and describing motion. If you know what you're doing, you can also use a V-T graph to find the distance covered during some period of time.
A horizontal line on a velocity-time (V-T) graph would show constant speed. This is because the slope of a V-T graph represents acceleration, and a horizontal line means zero acceleration, indicating constant speed.
Displacement is the area under the v-t graph.
The position at time t (and therefore the height of the p-t graph) will be the area under the v-t curve between time 0 and t.
distance
An x-t (position-time) graph shows how an object's position changes over time, while a v-t (velocity-time) graph shows how an object's velocity changes over time. In an x-t graph, the slope represents the object's velocity at that point, while in a v-t graph, the area under the curve represents the object's displacement.
An x-t graph shows displacement over time, and a v-t graph shows velocity over time. The combination of the two graphs can give you great detail about the motion of an object over a given period of time. For example, if an object moved 2 cm over 2 seconds on the x-t graph, that says nothing about what direction the object moved in, but if you combine that data with the v-t graph and see that over those 2 seconds the object had a positive acceleration, that means that the object was moving away from the origin of the graph.
Acceleration can be determined from a velocity-time graph by calculating the slope of the line on the graph. The steeper the slope, the greater the acceleration. If the graph is curved, acceleration can be calculated by finding the tangent to the curve at a specific point.
acceleration is the slope of the v t graph... so the acceleration is constant and negative. In other words, the object is slowing down at a constant rate.
A Compound Graph is an extension of a standard graph. Let G be a graph, G=(V,E) where V is a set of vertices and E is a set of edges, that is e = (v1, v2) in V2 A compound graph C is defined by a tree T=(V,F) where V is the same set as G and F are tree edges f=(v1,v2) in V2. C=(G,T) where G=(V,E) and T=(V,F) Furthermore, C has two additional constraints: e=(v1,v2) in E implies: 1) v1 is not on the path of v2 to the root of T AND 2) v2 is not on the path of v1 to the root of T. Intuitively, T defines a hierarchy. All the vertices sharing the same parent in T are in the same "group". The constraints state that you cannot have an edge connecting a vertex to one of its parent in the hierarchy.
To calculate the distance from a velocity-time graph, you can find the area under the graph. If the graph forms a triangle, you can use the formula for finding the area of a triangle (0.5 * base * height). If the graph forms other shapes, you can break down the area into smaller, more manageable shapes and calculate each separately before summing them up.
On a graph of velocity and time, a constant speed would appear as a straight horizontal line.