# Position-time graph

**Position-time graphs** are the most basic form of graphs in kinematics, which allow us to describe the motion of an object with respect to position and time. The \(y\)-axis of these graphs represent the distance traveled by the object, and the \(x\)-axis represents the time.

## Slope of a Position-time Graph

We know that the slope of a function is its derivative, and that the derivative of the displacement function is the velocity function, and thus the slope of a position-time graph gives us the velocity of the object:

\[(\text{Slope of a position time graph})=v=\dfrac{s_2-s_1}{t_2-t_1}.\]

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Find the velocity of the particle over the interval \((1,2)\).

We have seen that the slope of the position-time graph gives us the velocity over the time period. Thus, \[v=\dfrac{s_2-s_1}{t_2-t_1}=\dfrac{10-7.5}{2-1}=2.5\text{ (m/s)}.\]Note: We can see that the displacement of this object is given by the function \(s(t)=2.5t+5\). Thus, we can find the velocity of this function which is nothing but its derivative: \[v(t)=\dfrac{d}{dt}(2.5t+5)=2.5\text{ (m/s)}.\]

**Cite as:**Position-time graph.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/position-time-graph/