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1.] A particle is moving along a horizontal line and the velocity of the particle is given at various times in the table below.

t(hr)
1
4
9
10

v(t)(m//hr)
3
7
12
7

Is there a time
c,4 < c < 10, such that
a(c)=0 ? Explain your reasoning.

$1$ .] A particle is moving along a horizontal line and the velocity of the particle is given at various times in the table below. $\newline$ \begin{tabular}{|c|c|c|c|c|} $\newline$ \hline $\mathrm{t}(\mathrm{hr})$ & $1$ & $4$ & $9$ & $10$ \\ $\newline$ \hline $\mathrm{v}(\mathrm{t})(\mathrm{m} / \mathrm{hr})$ & $3$ & $7$ & $12$ & $7$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ Is there a time $\mathrm{c}, 4<c<10$ , such that $\mathrm{a}(\mathrm{c})=0$ ? Explain your reasoning.

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Probability of independent and dependent events

Full solution

Q.

1

.] A particle is moving along a horizontal line and the velocity of the particle is given at various times in the table below.

\newline

\begin{tabular}{|c|c|c|c|c|}

\newline

\hline

\mathrm{t}(\mathrm{hr})

&

1

&

4

&

9

&

10

\\

\newline

\hline

\mathrm{v}(\mathrm{t})(\mathrm{m} / \mathrm{hr})

&

3

&

7

&

12

&

7

\\

\newline

\hline

\newline

\end{tabular}

\newline

Is there a time

\mathrm{c}, 4<c<10

, such that

\mathrm{a}(\mathrm{c})=0

? Explain your reasoning.

Identify Time Interval: To find if there's a time $c$ where the acceleration $a(c) = 0$ , we need to look at the changes in velocity over the time intervals.
Velocity Changes Analysis: Between $t = 4$ and $t = 9$ , the velocity increases from $7$ m/hr to $12$ m/hr. This means the particle is accelerating.
Acceleration Determination: Between $t = 9$ and $t = 10$ , the velocity decreases from $12 \, \text{m/hr}$ to $7 \, \text{m/hr}$ . This means the particle is decelerating.
Acceleration Change Conclusion: If the velocity increases and then decreases, there must be a point where the acceleration changes from positive to negative, which means there is a point where the acceleration is $0$ .
Existence of Zero Acceleration: Therefore, there is a time $c$ , where $4 < c < 10$ , such that the acceleration $a(c) = 0$ .

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