Question

Given that $s\left(t\right)$measures the distance an object has travelled over time, explain what the expression $\frac{s\left(b\right)-s\left(a\right)}{b-a}$has to do with the distance formula $d=rt$.

Short answer

In expression $d=rt,r$represents the velocity of the object which is also represented by$\frac{s\left(b\right)-s\left(a\right)}{b-a}$.

Step-by-step solution

Step 1. Given information

The expression $\frac{s\left(b\right)-s\left(a\right)}{b-a}$

Distance formula $d=rt$

The distance an object has travelled over time is given by$s\left(t\right)$.

Step 2. Explanation

The expression $\frac{s\left(b\right)-s\left(a\right)}{b-a}$represent the distance travel by the object within two consecutive point of time. It will represent the rate of change of displacement with respect to time if $t=a$and $t=b$are two instantaneous points. Thus it will represent the velocity of the object or can be said $r=\frac{s\left(b\right)-s\left(a\right)}{b-a}$.

Hence, in the equation$d=rt,r$will represent the velocity of the object.