Exercise · ZW-TIME-DERIVATIVE-004 · ★★☆ Intermediate
What is the difference between \(\dot{\varphi}_t\) and an acceleration?
Choose one option.
A The first derivative only measures energy B Acceleration does not depend on time C The first derivative measures velocity; acceleration involves a higher-order time derivative D They are always the same object Show answer C. The first derivative measures velocity; acceleration involves a higher-order time derivative← Back to the question
Explanation \(\dot{\varphi}_t\) is the first time derivative and measures the velocity of the deformation. Acceleration corresponds to a higher-order derivative , such as \(\ddot{\varphi}_t\).
The time derivative \(\dot{\varphi}_t\) describes how a deformation changes as the time parameter \(t\) varies.
\[\dot{\varphi}_t=\frac{d\varphi_t}{dt}\]
More practice problems: time derivative