02Class 11 Physics

Motion in a Straight Line formulas

The equations of motion and graph rules for Motion in a Straight Line. Nearly all of this chapter comes down to choosing a sign convention and sticking to it.

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Definitions

Average velocity: $\displaystyle \bar v = \frac{\Delta x}{\Delta t}$
Instantaneous velocity: $\displaystyle v = \frac{dx}{dt}$
Instantaneous acceleration: $\displaystyle a = \frac{dv}{dt} = v\frac{dv}{dx}$

Equations of motion (constant acceleration)

First equation: $\displaystyle v = u + at$
Second equation: $\displaystyle s = ut + \tfrac12 at^2$
Third equation: $\displaystyle v^2 = u^2 + 2as$
Distance in the nth second: $\displaystyle s_n = u + \frac{a}{2}(2n - 1)$

Free fall and graphs

Falling from rest: $\displaystyle v = gt, \quad h = \tfrac12 gt^2, \quad v^2 = 2gh$
Relative velocity: $\displaystyle v_{BA} = v_B - v_A$
Reading graphs: $\displaystyle v = \text{slope of } x\text{-}t, \quad a = \text{slope of } v\text{-}t, \quad \Delta x = \text{area under } v\text{-}t$

Where students slip up

Using the equations of motion when acceleration isn't constant. If a depends on t or x, integrate instead.
Mixing signs for upward and downward motion. Choose one direction as positive at the start, and keep g negative or positive to match.
Confusing displacement with distance. The area under a v-t graph below the axis counts as negative displacement.

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