Question

1.) Explain the difference between average velocity and instantaneous velocity. Is it possible for these two values to be different?


2.) Given a position-time graph, describe how you would determine the average velocity and instantaneous velocity,

Answer 1

1.)

The instantaneous velocity at a given point can be defined as slope of the tangent of the curve drawn at a point while average velocity is equal to the slope of the secant line which intersects the function at the beginning and end of the interval.

average velocity = $\dfrac{X_f-X_i}{t_f-t_i}$

instantaneous velocity= $\dfrac{d(x(t))}{dt}$

These two velocities can same or different.

2.) In a position-time graph, average velocity can be determined by the formula $\dfrac{X_f-X_i}{t_f-t_i}$ or by finding the slope of the secant line which intersects the function at the beginning and end of the interval

and instantaneous velocity can be determined by $\dfrac{d(x(t))}{dt}$ at a particular point