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Kinematic Equations

Mahi Tuatahi

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 \newline & d = \frac{v_{i} + v_{f}}{2}t \newline & v_{f}^{2} = v_{i}^{2} + 2ad \newline & d = v_{i}t + \frac{1}{2}at^{2} \newline & d = v_{f}t - \frac{1}{2}at^{2} \end{aligned}

In your book, using a page in landscape, re-arrange each equation for each different variable!


Pātai Tahi:

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} \newline & && \text{Unknowns} \newline & && \text{Formula} \newline & && \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?

$v_{i} = 13ms^{-1}, a=0.6ms^{-2}, t=10s$


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?

$d = ?, v_{f} = \text{ not needed}$


Step Three – “formula”

Which formula does not include $v_{f}$?


Step Four - “substitute”

\begin{aligned} & d = v_{f}t + \frac{1}{2}at^{2} \newline & d = (13 \times 10) + (\frac{1}{2} \times 0.6 \times 10^{2}) \newline \end{aligned}


Step Five - “solve”

\begin{aligned} & d = v_{f}t + \frac{1}{2}at^{2} \newline & d = (13 \times 10) + (\frac{1}{2} \times 0.6 \times 10^{2}) \newline & d = 130 + 30 = 160m \end{aligned}


Pātai Rua

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?

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


Pātai Toru

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} \newline & && \text{Unknowns} \newline & && \text{Formula} \newline & && \text{Sub and Solve} \end{aligned}


Mahi Kāinga

Kinematics Question 1, due Monday 22nd/Tuesday 23rd


Whakawai/Practice