1 - Mathematical Foundations for Algebra-Based Physics Free Online FlashCards

What is the SI derived unit for force?

Force is measured in newtons: $\text{N}=\text{kg}\cdot\frac{\text{m}}{\text{s}^2}$.

Convert $72\ \frac{\text{km}}{\text{h}}$ to SI units.

$72\ \frac{\text{km}}{\text{h}}=20\ \frac{\text{m}}{\text{s}}$. Convert kilometers to meters and hours to seconds so unwanted units cancel.

Why is $v_f=v_i+a$ dimensionally invalid?

It is dimensionally invalid: velocity has dimensions $\frac{L}{T}$, while acceleration has dimensions $\frac{L}{T^2}$, so they cannot be added.

How does a scalar differ from a vector?

A scalar has magnitude only; a vector has both magnitude and direction.

What does a negative one-dimensional displacement signify?

The sign indicates direction relative to the chosen coordinate system; it is not an additional unit or separate physical quantity.

How are a vector's components found from its angle?

For a vector at angle $\theta$ above the positive $x$-axis, $A_x=A\cos\theta$ and $A_y=A\sin\theta$.

How do you find a vector's magnitude from its components?

The magnitude is $A=\sqrt{A_x^2+A_y^2}$. The component signs determine the vector's quadrant.

What does the slope of a position-versus-time graph represent?

The slope is average velocity: $\text{slope}=\frac{\Delta x}{\Delta t}=v_{\text{avg}}$.

What does area under a velocity-versus-time graph represent?

The signed area under a velocity-versus-time graph gives displacement. Area below the time axis contributes negatively.

Why solve a physics equation symbolically first?

Solve symbolically before substituting numbers. This exposes the equation's structure, reduces calculator errors, and helps track units.

What limiting-case check applies to $v_f=v_i+at$ when $t=0$?

Setting $t=0$ gives $v_f=v_i$, which is the expected initial-time result.

If speed doubles, how does kinetic energy change?

It becomes four times as large: $K'=\frac12m(2v)^2=4K$.