Kinematics and Dynamics

Core notes

Kinematics

Describing Movement - how is something moving?

Dynamics

Cause of Movement - why is something moving?

Scalars

Magnitude only (num values only) e.g. distance

Vectors

Magnitude and Direction e.g. Displacement

Distance

Distance of path, denoted as d, measured ONLY in m/km

Displacement

Direct distance from point a to b, denoted as s

Include exact true bearing and exact distance, measured ONLY in m/km

Speed

Scalar Quantity, measured in kmh^-1 or m^s-1, denoted as v

Formula: Vav = total d/t (v=d/t)

Velocity

Vector Quantity, measured in kmh^-1 or m^s-1. Denoted as u or →v.

Formula: u_av = total s/t (u = s/t)

Distance / Time Graph

y-axis: Distance

x-axis: Time

Tip: the slope of the distance time graph gives instantaneous speed, and it can NEVER be negative.

Displacement / Time Graph

y-axis: Displacement with given direction

x-axis: Time

Tip: the slope of the displacement time graph gives velocity, and it CAN be negative (negative velocity).

If it is not moving, there are NO direction (N/A)

Instantaneous Speed

Speed of an object at an exact time, t (the slope of the distance time graph). Can be in decimals.

Acceleration

Vector quantity, denoted as a.

Formula: Overall change in velocity/total time (a = Δu/Δt)

Second Formula: a = v-u/t, where v = final velocity, u = initial velocity, and t = time.

Third Formula: a = F/m, where F = net force, m = mass

Unit: ms^-2 (m/s²) e.g. 5m/s² = 5m / sec increase in velocity

Tip: Time = v-u/a

Veloctiy Time Graph

y-axis: Velocity

x-axis: Time

Tip: like displacement graph, any vector quantity graph can be negative, just like this one (negative velocity)

Slope = acceleration, Area (trapezium / triangle) = displacement

Positive Area = distance (get rid of negatives as it can’t be negative) = A1 + A2

Displacement (can accept negative) = A1 - A2 + direction (Negative = reverse direction, Positive = direction facing.)

Relationships of Graph that can be drawn from other

Distance - Time graph: can be drawn from Displacement - Time graph (but NOT reverse as there is not direction).

Speed - Time graph: can be drawn from distance time graph, and in reverse (no direction needed as both are scalars)

Displacement - Time graph: can be drawn from velocity - time graph, also in reverse (both are vectors).

Inertia: Newton’s 1st Law

An object remains at rest/constant motion, unless acted on by a net unbalanced external force.

Newton’s 2nd Law

The acceleration of an object produced by net force is directly proportional to acceleration and inversely proportional to mass.

Formula: F = ma, m = mass (kg), and a = acceleration (m/s²), F = net force (Newton, N).

Newton’s 3rd Law

Every force in nature has and equal and opposite reaction.

Force Diagram

Arrows from the centre of the object, depending on direction and amount of force, are in different sizes.

Friction: f=Fapplied​−Fnet​

Terminal Velocity

An object’s maximum velocity depends on several factors, such as air resistance, but the object is still moving.

Gravity Net Force

Relates to Newton’s 3rd Law, denoted as Fg

Formula: Fg = mg, where m = mass and g = gravitational acceleration on Earth (constant and varies on different planets, ~ 9.8m/s²)