U3AOS1 Topic 1: Kinematics

Scalar vs Vector

Scalar  quantities only have a magnitude .

Vector  quantities have a  magnitude AND a direction.

Displacement vs Distance

Displacement  is how far you are  from where you started.

Distance  is how far you  travel to get there.

Suppose you want to travel from the MCG to Mt Buller. The  car route  is the  distance   you would need to travel to get there.

All the car routes are $ 230 $km+ but the straight  black line  is the  displacement   which is only $ 150 $km.

Average Speed vs Velocity

Speed  is a scalar quantity related to  distance  and time

Velocity  is a vector quantity related to  displacement  and time

\[d = \text{distance}, t = \text{time}, s = \text{displacement} \]

\[\text{speed}_{avg} = \frac{d}{t} \]

\[\text{velocity} = v = \frac{ \Delta s}{ \Delta t} \]

IMPORTANT INFO

A common mistake in kinematics is forgetting that

IF  VELOCITY IS CONSTANT   THEN  ACCELERATION IS $0$

Justification:

- Acceleration  is the rate of change of velocity

- If the velocity is not changing (constant)

- Then $ \Delta v $   will be $0$

Plugging this into the formula gives:

\[a = \frac{ \Delta v}{ \Delta t} \]

\[a = \frac{0}{ \Delta t} \]

\[a = 0 \]

SUVAT Equations

\[v = u + at \]

\[v^2 = u^2 + 2as \]

\[s = ut + \frac{1}{2}at^2 \]

\[s = vt - \frac{1}{2}at^2 \]

\[s = \frac{1}{2} (u + v)t \]

The table below simplifies SUVAT and is really good to have in your cheat sheet to easily find which formula to use.

CONVERTING KM/H TO M/S

To go from $ \text{km/h} \rightarrow \text{m/s} $   DIVIDE   by $ 3.6 $

To go from $ \text{m/s} \rightarrow \text{km/h} $    MULTIPLY  by $ 3.6 $