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Kinematic Equations

Mahi Tuatahi 🔗

__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?

Te Whāinga Ako 🔗

  1. Be able to use 5 kinematic equations to solve problems.

Write the date and te whāinga ako in your book

Kinematic Equations 🔗

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!

Pātai Tahi 🔗

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”

$$ \begin{aligned} v_{i} &= 13ms^{-1}, a=0.6ms^{-2}, t=10s && \text{Knowns} \cr d &= ? && \text{Unknowns} \cr d &= v_{i}t + \frac{1}{2}at^{2} && \text{Formula} \cr d &= 13 \times 10 + \frac{1}{2} \times 0.6 \times 10^{2} && \text{Sub} \cr d &= 130 + 30 = 160m \end{aligned} $$

Practice / Whakawai 🔗

  1. A windsurfer initially travelling at $3 ms^{-1}$ is accelerated by a strong wind gust, at $0.08 ms^{-2}$. What would be the windsurfer’s speed when he has travelled $100 m$ since the wind gust started?
  2. What time does it take for an airplane to decelerate uniformly from $120 ms^{-1}$ to a stop if the distance covered along the runway is $1500 m$?

$$ \begin{aligned} & && \text{Knowns} \cr & && \text{Unknowns} \cr & && \text{Formula} \cr & && \text{Sub and Solve} \end{aligned} $$

Whakatika Rua 🔗

$$ \begin{aligned} v_{i} &= 3ms^{-1}, a=0.8ms^{-2}, d=100m && \text{Knowns} \cr v_{f} &= ? && \text{Unknowns} \cr v_{f}^{2} &= v_{i}^{2} + 2ad && \text{Formula} \cr v_{f}^{2} &= 3^{2} + 2\times0.08\times100 && \text{Sub and Solve} \cr v_{f} &= \sqrt{144} = 12ms^{-1} \end{aligned} $$

Whakatika Toru 🔗

$$ \begin{aligned} v_{i} &= 120ms^{-1}, v_{f} = 0ms^{-1}, d=1500m && \text{Knowns} \cr t &= ? && \text{Unknowns} \cr d &= \frac{v_{i} + v_{f}}{2}t && \text{Formula} \cr 1500 &= \frac{120 + 0}{2}t && \text{Sub and Solve} \cr 1500 &= 60t \cr t &= \frac{1500}{60} = 25s \end{aligned} $$

Whakawai/Practice 🔗