AP Physics C: Mechanics Unit 1: Kinematics Practice Exam

1. What is the resultant vector $\vec{C} = \vec{A} + \vec{B}$?

2. What is the approximate magnitude of vector $\vec{A}$?

3. The position of a particle moving in one dimension is given by the function $x(t) = 4t^3 - 6t^2 + 2$. What is the instantaneous velocity of the particle at $t = 2$ s?

4. A particle's velocity as a function of time is given by $\vec{v}(t) = (5t)\hat{i} - (2t^2)\hat{j}$. What is the particle's acceleration vector at $t = 3$ s?

5. The acceleration of an object is given by the function $a(t) = 6t$. If the object starts from rest at $t = 0$, what is its velocity at $t = 4$ s?

6. An object moves along the x-axis. Its position is given by $x(t) = 2t^2 - 8t$. What is the object's average velocity over the time interval from $t=1$ s to $t=3$ s?

7. What is the acceleration of the object at $t = 1$ s?

8. What is the displacement of the object during the first 2 seconds?

9. During which time interval is the object slowing down?

10. A ball is thrown vertically upward. At the highest point of its trajectory, which of the following is true?

11. An object is launched as a projectile with an initial velocity $\vec{v}_0$ at an angle $\theta$ above the horizontal. Air resistance is negligible. Which of the following statements is true regarding the object's acceleration during its flight?

12. What is the speed of the boat relative to an observer on the riverbank?

13. If the river is 80 m wide, how long does it take for the boat to cross the river?

14. A particle's position is described by the vector function $\vec{r}(t) = (3t^2)\hat{i} + (4t+1)\hat{j}$. What is the particle's speed at $t = 2$ s?

15. An object starts from rest and accelerates uniformly in a straight line. It travels a distance $d$ in a time $t$. If it were to accelerate with the same uniform acceleration for a time $2t$, what would be the total distance traveled?

16. An object starts with an initial velocity of $v_0 = -10$ m/s at $t=0$. What is the object's velocity at $t=2$ s?

17. What is the total change in the object's velocity from $t=0$ to $t=4$ s?

18. An observer in a train moving at a constant velocity throws a ball straight up into the air. Which of the following best describes the path of the ball as seen by an observer standing on the ground outside the train? (Neglect air resistance.)