1. Kinematics

Two-dimensional Motion — Quiz

Test your understanding of two-dimensional motion with 5 practice questions.

Practice Questions

Question 1

The position of a particle is given by the vector function $\vec{r}(t) = (A t^2 \hat{i} + B t^3 \hat{j}) \text{ m}$, where $A$ and $B$ are constants. What is the instantaneous acceleration vector of the particle?

Question 2

A projectile is launched from the ground with an initial speed $v_0$ at an angle $\theta$ above the horizontal. At what point in its trajectory is the magnitude of its velocity at a minimum (ignoring air resistance)?

Question 3

A boat travels at a velocity of $\vec{v}_{BW} = (4 \hat{i} + 3 \hat{j}) \text{ m/s}$ relative to the water. The water flows at a velocity of $\vec{v}_{WG} = (2 \hat{i} - 1 \hat{j}) \text{ m/s}$ relative to the ground. What is the velocity of the boat relative to the ground, $\vec{v}_{BG}$?

Question 4

A projectile is launched with an initial velocity of $(12 \hat{i} + 16 \hat{j}) \text{ m/s}$. What is the magnitude of its initial speed?

Question 5

An object's position is given by the vector function $\vec{r}(t) = (5t^2 \hat{i} + (4t - 2) \hat{j}) \text{ m}$. What is the velocity vector of the object at $t = 2 \text{ s}$?