# Kinematic Equations

12PHYS - Mechanics

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

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

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