3 - Two-Dimensional Kinematics Free Online FlashCards

How is a two-dimensional motion problem usually separated?

Choose axes first, then analyze the perpendicular components independently using one-dimensional kinematic equations that share the same time variable.

What is displacement?

Displacement is the vector from the initial position to the final position: $\Delta\vec r=\vec r_f-\vec r_i$.

What do slopes represent on motion graphs?

The slope of a position-versus-time graph gives velocity, while the slope of a velocity-versus-time graph gives acceleration.

How are a vector’s components found?

For a vector of magnitude $A$ at angle $\theta$, $A_x=A\cos\theta$ and $A_y=A\sin\theta$.

How are two vectors added?

Add corresponding components: $\vec A+\vec B=(A_x+B_x)\hat i+(A_y+B_y)\hat j$. Do not add magnitudes unless the vectors are parallel.

What is the definition of average velocity?

Average velocity equals displacement divided by elapsed time: $\vec v_{\text{avg}}=\frac{\Delta\vec r}{\Delta t}$.

How is constant-acceleration motion analyzed in two dimensions?

For constant acceleration, analyze the perpendicular components separately with one-dimensional kinematic equations; both components use the same time $t$.

What are the acceleration components of an ideal projectile?

For ideal projectile motion, $a_x=0$ and $a_y=-g$, so acceleration is vertically downward.

What is true at a projectile’s highest point?

At the highest point, $v_y=0$, but $v_x$ generally remains nonzero and acceleration is still $\vec a=-g\hat j$.

When does the standard projectile flight-time formula apply?

For equal launch and landing heights, $t_{\text{flight}}=\frac{2v_0\sin\theta}{g}$, assuming negligible air resistance.

How is the range of a horizontal launch determined?

For a horizontal launch, $v_{0y}=0$. Find the flight time from vertical motion, then use $\Delta x=v_{0x}t$.

How is relative velocity calculated?

Relative velocity is found by vector subtraction: $\vec v_{A/B}=\vec v_A-\vec v_B$.