Answer:
The average velocity is equal to the instantaneous velocity
Explanation:
The average velocity, [tex]\overline v[/tex], is given as follows;
[tex]\overline v = \dfrac{\Delta y}{\Delta t}[/tex]
Where;
Δy = The change in displacement
Δt = The change in time
The instantaneous velocity is the derivative found of the position of the object's displacement with respect to time
Therefore, the instantaneous velocity, [tex]v_{inst}[/tex] = The limit of the average velocity as the change in time becomes closer to zero
[tex]v_{inst} = \lim_{t \to 0} \left (\dfrac{\Delta y}{\Delta t} \right ) = \dfrac{dy}{dx}[/tex]
When the velocity is constant, the displacement time graph is a straight line graph, and the slope of the displacement-time graph which is the same as the velocity is constant and therefore, we have;
[tex]Slope \ of \ straight \ line \ graph = \dfrac{y_2 - y_1}{t_2 - t_1} = \dfrac{\Delta y}{\Delta t}= \dfrac{dy}{dx}[/tex]
Therefore, for constant velocity, we have, [tex]\overline v[/tex] = [tex]v_{inst}[/tex] the average velocity is equal to the instantaneous velocity.
