# Kinematic Equations

12PHYS - Mechanics

Finn LeSueur

2020

## 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

- 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

- Worksheet #5 (Q1, 2 and 3 only)
- Homework booklet Q2, Q3, Q4, Q5a, Q6a-6b, Q7