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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

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*}

First we must find convert mph to m/s

Δv=\begin{align*}\Delta v =\end{align*} 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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