12PHYS - Mechanics
Finn Le Sueur
2024
Head up your book with the title: Kinematics
Try and solve this problem:
A car initially travelling at \(13ms^{-1}\) rolls down a straight slope, accelerating at \(0.6 ms^{-2}\) for \(10 s\). How far does the car travel in this time?
Write the date and te whāinga ako in your book
Five variables - five equations!
\[ \begin{aligned} v_{f} &= v_{i} + at \cr d &= \frac{v_{i} + v_{f}}{2}t \cr v_{f}^{2} &= v_{i}^{2} + 2ad \cr d &= v_{i}t + \frac{1}{2}at^{2} \cr d &= v_{f}t - \frac{1}{2}at^{2} \end{aligned} \]
On your whiteboard re-arrange each equation for each different variable, the add the manipulated form to your sheet!
Let’s try that starter question again. A car initially travelling at \(13ms^{-1}\) rolls down a straight slope, accelerating at \(0.6 ms^{-2}\) for \(10 s\). How far does the car travel in this time?
\[ \begin{aligned} & && \text{Knowns} \cr & && \text{Unknowns} \cr & && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} \]
Step One – “knowns”
A car initially travelling at \(13ms^{-1}\) rolls down a straight slope, accelerating at \(0.6 ms^{-2}\) for \(10 s\). How far does the car travel in this time?
\[ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr & && \text{Unknowns} \cr & && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} \]
Step Two – “unknowns”
A car initially travelling at \(13ms^{-1}\) rolls down a straight slope, accelerating at \(0.6 ms^{-2}\) for \(10 s\). How far does the car travel in this time?
\[ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr d &= ? && \text{Unknowns} \cr & && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} \]
Step Three – “formula”
Which formula includes the three knowns and one unknown?
\[ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr d &= ? && \text{Unknowns} \cr d &= v_{i}t + \frac{1}{2}at^{2} && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} \]
Step Four - “substitute”
\[ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr d &= ? && \text{Unknowns} \cr d &= v_{i}t + \frac{1}{2}at^{2} && \text{Formula} \cr d &= 13 \times 10 + \frac{1}{2} \times 0.6 \times 10^{2} && \text{Sub} \end{aligned} \]
Step Five - “solve”
\[ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr d &= ? && \text{Unknowns} \cr d &= v_{i}t + \frac{1}{2}at^{2} && \text{Formula} \cr d &= 13 \times 10 + \frac{1}{2} \times 0.6 \times 10^{2} && \text{Sub} \cr d &= 130 + 30 = 160m \end{aligned} \]
\[ \begin{aligned} & && \text{Knowns} \cr & && \text{Unknowns} \cr & && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} \]
\[ \begin{aligned} v_{i} &= 3ms^{-1}, a=0.8ms^{-2}, d=100m && \text{Knowns} \cr v_{f} &= ? && \text{Unknowns} \cr v_{f}^{2} &= v_{i}^{2} + 2ad && \text{Formula} \cr v_{f}^{2} &= 3^{2} + 2\times0.08\times100 && \text{Sub and Solve} \cr v_{f} &= \sqrt{144} = 12ms^{-1} \end{aligned} \]
\[ \begin{aligned} v_{i} &= 120ms^{-1}, v_{f} = 0ms^{-1}, d=1500m && \text{Knowns} \cr t &= ? && \text{Unknowns} \cr d &= \frac{v_{i} + v_{f}}{2}t && \text{Formula} \cr 1500 &= \frac{120 + 0}{2}t && \text{Sub and Solve} \cr 1500 &= 60t \cr t &= \frac{1500}{60} = 25s \end{aligned} \]