Question

what does the tangent at a point to the position time graph for an object in non-uniform motion along a straight line represents

Answer 1

Question 31522

The position time graph is the graph of the function $x(t)$ if body moves along a straight line along ox. By definition, velocity at given time $t^{\prime}$ is the derivative of $x$ with respect to $t$ at moment $t^{\prime}$: $v(t^{\prime})=x^{\prime}|_{t=t^{\prime}}$. Since the derivative represents the slope of the tangent to the graph at given point, the slope of the tangent at a point $k=\tan\phi=x^{\prime}(t)$ to the $x(t)$ graph represents the velocity of the object at given moment of time.