Mahi Tuatahi: Kahoot! ^🔗

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https://create.kahoot.it/kahoots/my-kahoots/folder/2f5a1b63-53ba-4c44-9678-287ca08d461d

What is Acceleration? ^🔗

Acceleration is how quickly the velocity changes.

e.g. A supercar will reach 50km/hr faster than a cyclist. That is to say, the supercar has a greater acceleration.

Calculating Acceleration ^🔗

$$ \begin{aligned} acceleration &= \frac{\text{change in speed}}{\text{change in time}} \cr a &= \frac{\Delta v}{\Delta t} \cr \end{aligned} $$

• Velocity ($v$) has units meters per second ($ms^{-1}$)
• Time ($t$) has units seconds ($s$)
• Acceleration ($a$) has units meters per second per second ($m/s^{2}$ or $ms^{-2}$)

Example ^🔗

$a = 2.5ms^{-2}$. A cyclist accelerates from rest. They will gain $2.5ms^{-1}$ of velocity every second!

Rearranging Equations ^🔗

Work with a partner to rearrange $a=\frac{\Delta v}{\Delta t}$ in your book where $v$ and $t$ are the subject of the equation.

Whakatika ^🔗

$$ \begin{aligned} a &= \frac{\Delta v}{\Delta t} && \text{d is divided by t} \cr v \times \Delta t &= \Delta d && \text{Multiply both sides by t} \cr \end{aligned} $$

$$ \begin{aligned} a &= \frac{\Delta v}{\Delta t} && \text{v is divided by t} \cr a \times \Delta t &= \Delta v && \text{Multiply both sides by t} \cr \Delta t &= \frac{\Delta v}{a} && \text{Divide both sides by a} \end{aligned} $$

Question 1 ^🔗

A bee starts at rest and takes off from a flower and reaches a velocity of $0.75ms^{-1}$ in $0.5s$. Calculate it’s acceleration.

Question 1: Answer ^🔗

1. Knowns: $\text{time (t)} = 0.5s$, $\Delta v = v_{f} - v_{i} = 0.75 - 0 = 0.75ms^{-1}$
2. Unknowns: $\text{acceleration (a)}$
3. Formula: $a = \frac{\Delta v}{\Delta t}$
4. Substitute: $a = \frac{0.75}{0.5}$
5. Solve: $v = 1.5\frac{m}{s^{2}} = 1.5ms^{-2}$

Question 2 ^🔗

A Bugatti Veyron accelerates from rest at $27.77ms^{-2}$ for $2.6s$. How fast is it travelling at after 2.6 seconds?

Question 2: Answer ^🔗

1. Knowns: $\text{time (t)} = 2.6s$, $\text{acceleration (a)} = 27.77ms^{-2}$
2. Unknowns: $\text{final velocity } v_{f}$
3. Formula: $a = \frac{\Delta v}{\Delta t} = \frac{v_{f} - v_{i}}{\Delta t}$
4. Substitute: $27.77 = \frac{v_{f} - 0}{2.6}$
5. Solve: $27.77 \times 2.6 = v_{f} = 72.2ms^{-1}$

Question 3 ^🔗

A skydiver at rest jumps out of a plane. They accelerate at $9.8ms^{-2}$ until they reach a terminal velocity of $54ms^{-2}$. How long does it take them to reach this speed?

Question 3: Answer ^🔗

1. Knowns: $\text{acceleration (a)} = 9.8ms^{-2}$, $\text{final velocity } (v_{f}) = 45ms^{-1}$
2. Unknowns: $\text{time (t)}$
3. Formula: $a = \frac{\Delta v}{\Delta t} = \frac{v_{f} - v_{i}}{\Delta t}$

$$ \begin{aligned} 9.8 &= \frac{54 - 0}{t} \cr 9.8 \times t &= 54 \cr t &= \frac{54}{9.8} = 5.51s \end{aligned} $$

Question 4 ^🔗

A runner is approaching the finish line, moving at $5.55ms^{-1}$ but needs to sprint to pass the person just in front of them to get 1st place. They accelerate for $3s$ to reach $6.3ms^{-1}$. What is their acceleration?

Question 4: Answer ^🔗

1. Knowns: $v_{i} = 5.55ms^{-1}$, $v_{f} = 6.3ms^{-1}$, $\Delta t = 3s$
2. Unknowns: $\text{acceleration (a)}$
3. Formula: $a = \frac{\Delta v}{\Delta t} = \frac{v_{f} - v_{i}}{\Delta t}$

$$ \begin{aligned} a &= \frac{6.3 - 5.55}{3} \cr a &= \frac{0.75}{3} = 0.25ms^{-2} \end{aligned} $$

Mahi Kāinga / Homework ^🔗

• Due Monday, March 21st: Mahi Kāinga Booklet Q2, Q3, Q1
• Ask me for help with your mahi kāinga at any time!
• Do the work in your exercise book!