Question

If $s=f\left(t\right)$ denotes the position of a particle at time t, the derivative $f\text{'}\left(c\right)$is the ______ of the particle at c.

Short answer

If $s=f\left(t\right)$ denotes the position of a particle at time t, the derivative $f\text{'}\left(c\right)$ is thevelocity of the particle atc.

Step-by-step solution

Step 1. Given Information

Velocity is defined as the rate of change of position with respect to time.

Step 2. Filling the blank

As it is given that the position of the particle is $s=f\left(t\right)$ at time t, then the rate of change of the position is

$f\text{'}\left(c\right)=\underset{t\to c}{\lim }\frac{f\left(t\right)-f\left(c\right)}{t-c}$, and the rate of change of the position is called velcoity.

So, if $s=f\left(t\right)$ denotes the position of a particle at time t,the derivative $f\text{'}\left(c\right)$is the velocity of the particle atc.