Question

1 multiple choice 0.5 points
video (timestamp ~3:07): the video shows secant lines $\frac{delta x}{delta t}$ getting closer to a tangent line as $delta t \to 0$. what does the slope of the tangent line represent?

• average speed over the whole motion
• instantaneous velocity at that time
• instantaneous acceleration
• average velocity over the whole motion

Explanation:

The slope of a secant line $\frac{\Delta x}{\Delta t}$ represents average velocity over a time interval $\Delta t$. As $\Delta t \to 0$, the secant line approaches a tangent line, whose slope captures the velocity at a single instant in time, not an average over an interval, nor acceleration.

Answer:

instantaneous velocity at that time