Question

question 3
when using calculus to define the instantaneous velocity, \v\, which one of the following statements is false:
v is \the derivative of position with respect to time\
v \equals dx divided by dt\
$v = \frac{dx}{dt}$
$v=lim_{t
ightarrow0}\frac{delta x}{delta t}$

Explanation:

Instantaneous velocity \(v\) is defined as the derivative of position \(x\) with respect to time \(t\), which can be written as \(v=\frac{dx}{dt}\) or \(v = \lim_{\Delta t
ightarrow0}\frac{\Delta x}{\Delta t}\). The first three options correctly express this concept. The fourth option \(v=\frac{d x}{d t}\) (repeated in a different format) is also correct. There seems to be an error in the question - all the given statements are true in the context of calculus - based - definition of instantaneous velocity. But if we assume there is a mis - typing in the options and we consider the standard definition, all are correct except if we mis - interpret the notation in an incorrect way. Since the limit definition of the derivative \(v=\lim_{\Delta t
ightarrow0}\frac{\Delta x}{\Delta t}\) is equivalent to \(v = \frac{dx}{dt}\), and \(v\) is the derivative of position with respect to time.

Answer:

There is no false statement among the given options.