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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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Velocity and Acceleration

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

Key Equations

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

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

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

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

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

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

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

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 \begin{align*} 5 \ m/s^2 \end{align*}5 m/s2 indicates that the velocity is increasing by \begin{align*} 5 m/s \end{align*}5m/s 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 \begin{align*}m/s^2\end{align*}m/s2?

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

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

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

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

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

Plug n’ Chug: Step 1: Convert km/hr to 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*}vf=(160kmhr)(1,000 m1 km)(1 hr3,600 s)=44.4 m/s

Step 2: Solve for average acceleration:

\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*}aavg=Δvt=vfvit=44.4 m/s0 m/s0.8 s=56 m/s2

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

Watch this Explanation

Simulation

The Moving Man (PhET Simulation)

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?

Answers

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

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