8. Applications of Integration

Connecting Position, Velocity, And Acceleration Of Functions Using Integrals — Quiz

Test your understanding of connecting position, velocity, and acceleration of functions using integrals with 5 practice questions.

Practice Questions

Question 1

A particle has velocity $v(t)$. What does $\int_a^b v(t)\,dt$ represent?

Question 2

If a particle's acceleration is $a(t)$, what does $\int_a^b a(t)\,dt$ represent?

Question 3

A particle has velocity $v(t)=3$ for $0\le t\le 2$ and position $s(0)=5$. What is $s(2)$?

Question 4

If $v(t)\ge 0$ for all $t$ in $[a,b]$, what can be concluded about the position function $s(t)$ on that interval?

Question 5

If acceleration $a(t)$ is positive on an interval, what happens to velocity $v(t)$ on that interval?