Scalars $\text{vs.}$ $\text{Vectors}$ 🧭
$\text{Kinematics}$ requires distinguishing between two types of quantities: $\text{Scalars}$ and $\text{Vectors}$.
$\text{Scalar}$
Has $\text{magnitude}$ ($\text{size}$) $\text{only}$.
$$\text{Examples}: \text{Distance} (d), \text{Speed} (v), \text{Time} (t)$$
$\text{Vector}$
Has $\text{magnitude}$ ($\text{size}$) $\text{and}$ $\text{direction}$.
$$\text{Examples}: \text{Displacement} (\vec{d}), \text{Velocity} (\vec{v}), \text{Acceleration} (\vec{a})$$
Key $\text{Kinematic}$ $\text{Concepts}$ 📏
$\text{Displacement}$ ($\vec{d}$)
Change in $\text{position}$: $\vec{d} = \vec{x}_f - \vec{x}_i$. A $\text{vector}$.
$\text{Speed}$ ($\text{v}$)
Rate of change of $\text{distance}$ ($\text{v} = d/t$). A $\text{scalar}$.
$\text{Velocity}$ ($\vec{v}$)
Rate of change of $\text{displacement}$: $\vec{v} = \Delta \vec{d} / \Delta t$. A $\text{vector}$.
$\text{Acceleration}$ ($\vec{a}$)
Rate of change of $\text{velocity}$: $\vec{a} = \Delta \vec{v} / \Delta t$. A $\text{vector}$. $\text{Units}: \text{m}/\text{s}^2$.
The $\text{Big}$ $\text{Three}$ $\text{Kinematic}$ $\text{Equations}$ formulae
These equations apply only to motion with **$\text{constant}$ $\text{acceleration}$** ($\text{uniform}$ $\text{acceleration}$):
1. $\text{Velocity}$-$\text{Time}$
Final velocity ($v_f$) is determined by initial velocity ($v_i$), acceleration ($a$), and time ($t$).
$$\vec{v}_f = \vec{v}_i + \vec{a}t$$2. $\text{Displacement}$-$\text{Time}$ $\text{v} \text{formula}$
Displacement ($\Delta \vec{d}$) is determined by initial velocity, acceleration, and time.
$$\Delta \vec{d} = \vec{v}_i t + \frac{1}{2}\vec{a}t^2$$3. $\text{Velocity}$-$\text{Displacement}$
Final velocity is determined by initial velocity, acceleration, and displacement ($\text{eliminates}$ $\text{time}$).
$$\vec{v}_f^2 = \vec{v}_i^2 + 2\vec{a}\Delta \vec{d}$$⚡ $\text{Concept}$ $\text{Check}$ $\text{Challenge}$!
Determine whether the following quantity or scenario is a **$\text{Scalar}$** (Magnitude $\text{only}$) or a **$\text{Vector}$** (Magnitude $\text{and}$ $\text{Direction}$).
Reset Your Score
If you want to play again, you can reset your score here.