Answered

\begin{tabular}{|c|c|c|c|c|c|}
\hline
\begin{tabular}{l}
\# of \\
washers
\end{tabular} & \begin{tabular}{l}
Initial \\
velocity \\
[tex]$v_1$[/tex] \\
( [tex]$m / s$[/tex] )
\end{tabular} & \begin{tabular}{l}
Final \\
velocity \\
[tex]$\underset{( m / s )}{v_2}$[/tex]
\end{tabular} & \begin{tabular}{l}
Time to travel \\
[tex]$0.25 m$[/tex] \\
[tex]$t_1$[/tex] \\
(s)
\end{tabular} & \begin{tabular}{l}
Time to travel \\
[tex]$0.50 m$[/tex] \\
[tex]$t_2$[/tex] \\
(s)
\end{tabular} & \begin{tabular}{l}
Acceleration \\
[tex]$a=\underset{\left( m / s^2\right)}{\left(v_2-v_1\right) / t_1}$[/tex]
\end{tabular} \\
\hline
2 & 0.13 & 0.36 & 1.92 & 2.61 & \\
\hline
\end{tabular}

The acceleration of the car with the data in the table above would be [tex]$\square$[/tex] [tex]$m / s^2$[/tex].

If the applied force were cut in half, what do you predict the acceleration would be? [tex]$\square$[/tex] [tex]$m / s^2$[/tex]



Answer :

GinnyAnswer
Sure! Let's work through this problem step-by-step.

### Given Data
- Initial velocity, \( v_1 = 0.13 \, \text{m/s} \)
- Final velocity, \( v_2 = 0.36 \, \text{m/s} \)
- Time for the car to travel \( 0.25 \, \text{m} \), \( t_1 = 1.92 \, \text{s} \)

### Step-by-Step Solution

1. Calculate the acceleration:

The formula to calculate acceleration is:
[tex]\[ a = \frac{{v_2 - v_1}}{{t_1}} \][/tex]

- Substitute the given values:
[tex]\[ a = \frac{{0.36 \, \text{m/s} - 0.13 \, \text{m/s}}}{1.92 \, \text{s}} \][/tex]

2. Simplify the expression to find acceleration:

- Calculate the difference in velocity:
[tex]\[ 0.36 \, \text{m/s} - 0.13 \, \text{m/s} = 0.23 \, \text{m/s} \][/tex]

- Divide by the time:
[tex]\[ \frac{0.23 \, \text{m/s}}{1.92 \, \text{s}} = 0.11979166666666666 \, \text{m/s}^2 \][/tex]

So, the acceleration of the car is:
[tex]\[ a = 0.11979166666666666 \, \text{m/s}^2 \][/tex]

2. Predict the new acceleration if the force is cut in half:

The acceleration is directly proportional to the force (from Newton's Second Law: \( F = ma \)). If the force is halved, the acceleration will also be halved. Therefore:
[tex]\[ a_{\text{new}} = \frac{a}{2} = \frac{0.11979166666666666 \, \text{m/s}^2}{2} = 0.05989583333333333 \, \text{m/s}^2 \][/tex]

### Final Responses

- The acceleration of the car with the given data is:
[tex]\[ 0.11979166666666666 \, \text{m/s}^2 \][/tex]

- If the applied force were cut in half, the new acceleration would be:
[tex]\[ 0.05989583333333333 \, \text{m/s}^2 \][/tex]

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