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# Velocity and Acceleration

## The speed and direction of a moving object and how that rate changes over time.

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Practice Velocity and Acceleration

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Velocity and Acceleration

Students will learn the meaning of acceleration, how it is different than velocity and how to calculate average acceleration.

### Key Equations

v=\begin{align*}v =\end{align*} velocity (m/s)

vi=\begin{align*}v_i =\end{align*} initial velocity

vf=\begin{align*}v_f =\end{align*} final velocity

Δv=\begin{align*}\Delta v =\end{align*} change in velocity =vfvi\begin{align*}= v_f - v_i\end{align*}

vavg=ΔxΔt\begin{align*}v_{avg} = \frac{\Delta x}{\Delta t}\end{align*}

a=\begin{align*}a =\end{align*} acceleration (m/s2)\begin{align*}(m/s^2)\end{align*}

aavg=ΔvΔt\begin{align*}a_{avg} = \frac{\Delta v}{\Delta t}\end{align*}

Guidance
• Acceleration is the rate of change of velocity. So in other words, acceleration tells you how quickly the velocity is increasing or decreasing. An acceleration of 5 m/s2\begin{align*} 5 \ m/s^2 \end{align*} indicates that the velocity is increasing by 5m/s\begin{align*} 5 m/s \end{align*} in the positive direction every second.
• Deceleration is the term used when an object’s speed (i.e. magnitude of its velocity) is decreasing due to acceleration in the opposite direction of its velocity.

#### Example 1

A Top Fuel dragster can accelerate from 0 to 100 mph (160 km/hr) in 0.8 seconds. What is the average acceleration in m/s2\begin{align*}m/s^2\end{align*}?

Question: aavg=? [m/s2]\begin{align*}a_{avg} = ? \ [m/s^2]\end{align*}

Given: vi=0 m/s\begin{align*}v_i = 0 \ m/s\end{align*}

vf=160 km/hr\begin{align*}{\;} \qquad \ \ v_f = 160 \ km/hr\end{align*}

t=0.8 s\begin{align*}{\;} \qquad \ \quad t = 0.8 \ s\end{align*}

Equation: aavg=Δvt\begin{align*}a_{avg} = \frac{\Delta v }{t}\end{align*}

Plug n’ Chug: Step 1: Convert km/hr to m/s

vf=(160kmhr)(1,000 m1 km)(1 hr3,600 s)=44.4 m/s\begin{align*}v_f = \left( 160 \frac{km}{hr} \right ) \left( \frac{1,000 \ m}{1 \ km} \right ) \left ( \frac{1 \ hr}{3,600 \ s} \right ) = 44.4 \ m/s\end{align*}

Step 2: Solve for average acceleration:

aavg=Δvt=vfvit=44.4 m/s0 m/s0.8 s=56 m/s2\begin{align*}a_{avg} = \frac{\Delta v}{t} = \frac{v_f - v_i}{t} = \frac{44.4 \ m/s - 0 \ m/s}{0.8 \ s} = 56 \ m/s^2\end{align*}

Answer: \begin{align*}\boxed {\mathbf{56 \ m/s^2}}\end{align*}

### Time for Practice

1. Ms. Reitman’s scooter starts from rest and accelerates at \begin{align*}2.0 m/s^2\end{align*}. What is the scooter's velocity after 1s? after 2s? after 7s?

1. 2 m/s, 4 m/s, 14 m/s

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