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Mechanical Engineering QUESTION #2515
Question 1
A particle moves along a curve. Its position vector is \(\mathbf{r}(t)\). The velocity is defined as:
  • The second derivative \(\ddot{\mathbf{r}}\)
  • The time derivative \(\dot{\mathbf{r}} = \frac{d\mathbf{r}}{dt}\)✔️
  • The magnitude \(|\mathbf{r}|\) divided by time
  • The integral of acceleration
Correct Answer Explanation
By definition, velocity of a point P is \(\mathbf{v} = \frac{d\mathbf{r}}{dt}\), the first time derivative of the position vector. Acceleration is the second derivative \(\mathbf{a} = \ddot{\mathbf{r}}\).