Question

Given the velocity function v of an object moving along a​ line, explain how definite integrals can be used to find the displacement of the object

Answer 1

Answer:

Expression of displacement will be $s(t)=\int_{t_0}^{t}v(t)dt$

Explanation:

Let the velocity $v(t)$ is function of time means when time changes then velocity also changes

We have to find the expression of definite integral to find the displacement

Displacement is ti,e integral of velocity in given period of time

Let the object starts moving at time $t=t_0$ and move to the time $t=t$

Then displacement is give by

$s(t)=\int_{t_0}^{t}v(t)dt$