Particle Motion for the AP Exam

A particle is traveling on a horizontal axis with position function given as $$x\left(t\right)=t^2-6t+3$$ for $$t\ge0$$ . At what time does the particle change directions?

Given the position function $$s\left(t\right)=t^3+3t^2-45t$$  , determine if the particle is speeding up or slowing down at t=2.

Given Particle A at t=2 has a position of 2, a velocity of -3, and an acceleration of 4, Which of the following Particles would be APPROACHING particle A (both particle A and the other particle are headed toward each other)?

Given the graph of velocity of a particle, which of the following would be a negative value?

Calculator: A particle moves along a line so that its acceleration for $$t\ge0$$ is $$\frac{t+3}{\sqrt{\ t^3+1}}$$ . If the particle's velocity at t=0 is 5, what is the velocity of the particle at t=3?

Calculator: If the velocity of a particle is given by $$v\left(t\right)=e^{\cos\left(t\right)}$$ what is the average velocity on [0,4]?

Which of the following determines speed?