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Acceleration, Velocity, and Position Along a Plane Curve (Integration)

Using vector-valued functions to solve problems related to position and velocity of objects.

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Coaster Calculations

Have you ever calculated the velocity of a rollercoaster you rode? The odds are that the rush of the rollercoaster left you unable to do so. So nows your chance

This rollercoaster went from 0-135 mph in 3.15 seconds

The equations you can use are 

\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

First we must find convert mph to m/s 

\begin{align*}\Delta v =\end{align*}Δv= 135 mph=60.44 m

so (60.44/3.15)=19.16m/s

Therefore the average velocity is 19.16

Creative Questioning:

1. How would you change the outcome of this question?(which factor would you have to change?

2.What is the relation between velocity and time?

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