Mechanics Revision: Key Concepts, Equations, and Graphical Rules

A set of 40 vocabulary flashcards covering key mechanics principles, graphical interpretations, equations of motion, vectors, and projectile rules.

Finding Force from Displacement

Differentiate twice with respect to $t$, then multiply by mass.

Force-Related Kinematic Quantity

Acceleration

Absolute Area Under a Velocity-Time Graph

Distance travelled

Average Velocity Formula

Change in displacement / time taken

Maximum Displacement (Mathematical Translation)

$$v = \frac{dr}{dt} = 0$$

Horizontal Section Above the t-Axis on a Velocity-Time Graph

Moving in the positive direction at a constant speed.

Reaching Furthest Point (Velocity-Time Graph Feature)

Root (crossing the $t$-axis)

Change in Direction (Displacement-Time Graph Feature)

Turning point

Vector (a, b) Parallel to the j Direction

$$a = 0$$

First Step in Variable Acceleration with an Expression for v

Sketch the $v$-$t$ graph (on your calculator if possible)

Magnitude of Acceleration (Quantity Type)

A scalar

Range of a Projectile (Mathematical Translation)

Find $x$ when $y = \text{final height} - \text{initial height}$ (by finding $t$ first)

Maximum/Minimum Velocity (Mathematical Translation)

$$a = \frac{dv}{dt} = 0$$

Velocity on a Displacement-Time Graph

Gradient

Finding Acceleration from Velocity Function

Differentiate

Finding Average Speed from a Displacement-Time Graph

Add up the total distance travelled and divide by the total time taken.

Speed on a Displacement-Time Graph

$$|\text{Gradient}|$$

Trajectory / Cartesian Equation of a Projectile (3-Step Method)

1. Find expressions for $x$ and $y$ at time $t$.
2. Make $t$ the subject of the $x$ equation.
3. Substitute this into the $y$ equation.

Vector (a, b) Points South-West

$a = b$ (and $a, b < 0$)

Vector (a, b) Points North-West

$a = -b$ where $b > 0$

Curved Velocity-Time Graph Realism

Because acceleration (and force) do not change instantaneously.

Vector (a, b) Points West

$b = 0$ (and $a < 0$)

Instantaneous Speed in Two Dimensions

Find the magnitude of its instantaneous velocity.

Downward Sloping Section Below the t-Axis on a Displacement-Time Graph

Moving away from the origin, further in the negative direction.

Finding Average Speed from a Velocity-Time Graph

Total absolute area / time taken

Acceleration of a Projectile in Vector Form

$$(0, -g)$$

Beginning a Projectiles Question (2 Steps)

1. Create horizontal and vertical suvat lists.
2. Fill in $u$ and $a$ in both columns.

Average Speed Formula

Total distance travelled / total time taken

Passing Through the Origin (Displacement-Time Graph Feature)

Root (crossing the $t$-axis)

Position Vector Under Constant Acceleration

$$r = r_0 + ut + \frac{1}{2}at^2$$

Finding Velocity from Acceleration Function

Integrate

Vector (a, b) Points South-East

$b = -a$ where $a > 0$

Gradient of a Displacement-Time Graph

Velocity

Distance Travelled (Velocity-Time Graph Feature)

Absolute area

Finding Average Velocity from a Displacement-Time Graph

(Final displacement - initial displacement) / time taken

"Initially at Rest" (Variable Acceleration)

When $t = 0$, $v = 0$

"Initially at Rest" (Constant Acceleration)

$$u = 0$$

Horizontal Equation for Projectiles

$$x = ut$$

Assumption of No Air Resistance on a Projectile

Weight is the only force acting and therefore the acceleration is $(0, -g)$

Signed Area Under a Velocity-Time Graph

Displacement