Question

2 multiple choice 0.5 points
video (timestamp -1:48) / reading: the board shows $v = \frac{dx}{dt}$. which expression is the definition of instantaneous velocity $v_x$?
$v_x = \frac{(total\\ distance)}{(total\\ time)}$
$v_x = \lim_{\delta t \to 0} \frac{\delta x}{\delta t}$
$v_x = \frac{\delta t}{\delta x}$
$v_x = area\\ under\\ an\\ x-t\\ graph$

Explanation:

• The first option defines average speed, not instantaneous velocity.
• Instantaneous velocity is the limit of the average velocity $\frac{\Delta x}{\Delta t}$ as the time interval $\Delta t$ approaches 0, which matches the definition of the derivative $v = \frac{dx}{dt}$.
• The third option is the reciprocal of average velocity, which has no relation to instantaneous velocity.
• The area under an x-t graph represents displacement, not velocity.

Answer:

v_x = lim(Δt→0) (Δx/Δt)