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 $v(t)=3t^2$ on $0\le t\le 2$. What is its displacement over this interval?

Question 2

If a particle's acceleration is $a(t)=4$ and its velocity at $t=0$ is $v(0)=1$, what is $v(t)$?

Question 3

What does $\int_a^b v(t)\,dt$ represent for a particle with velocity $v(t)$?

Question 4

For a particle with velocity $v(t)=2t-4$ on $0\le t\le 5$, on what interval is the position decreasing?

Question 5

If the acceleration $a(t)$ is positive on an interval, what does that tell you about velocity $v(t)$ on that interval?