Q. 5 - Calculus

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 $d=rt$.

Step-by-Step Solution

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 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.