# Question #93b0e

Aug 6, 2017

${V}_{i} = \lim t \to 0 \left(\frac{\triangle d}{\triangle t}\right)$ is the equation defining the velocity of a moving object at a particular instant in time, and like photographing a speeding car, it is a snapshot.

#### Explanation:

${V}_{i}$ is the velocity of the object at that instant or instantaneous velocity.

$\lim t \to 0$ states that the time we are observing the velocity is limited, and is now so short, that it is approaching $0.000000 \sec$

$\left(\frac{\triangle d}{\triangle t}\right)$ informs us that the velocity is a function of the distance divided by the time, and since we are considering velocity here the direction must also be defined.

The $\triangle '$s tell us the function refers to the change in something, in this case the change in distance divided by the change in time.

As you might suspect, since the $\triangle t$ observing time is so short, the $\triangle d$ distance travelled will also be short compared to the overall distance travelled. As a result, we can be sure that the calculation of the instantaneous velocity will be correct for the moving object, which may be either accelerating, decelerating, or moving at a constant velocity.