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The table provides data on the initial velocity, final velocity, time to travel specific distances, and acceleration for a car with washers added to the string.

| # of washers | Initial velocity [tex]\( v_1 \)[/tex] (m/s) | Final velocity [tex]\( v_2 \)[/tex] (m/s) | Time to travel 0.25 m [tex]\( t_1 \)[/tex] (s) | Time to travel 0.50 m [tex]\( t_2 \)[/tex] (s) | Acceleration [tex]\( a \)[/tex] (m/s²) |
|--------------|--------------------------------|------------------------------|---------------------------------|---------------------------------|-----------------------------|
| 1 | 0.11 | 0.28 | 2.23 | 3.13 | 0.19 |
| 2 | 0.13 | 0.36 | 1.92 | 2.61 | |

Calculate the acceleration of the car with two washers added to the string.

Sagot :

To find the acceleration of the car with two washers added to the string, we will use the following given data:

- Initial velocity [tex]\( v_1 \)[/tex] = 0.13 m/s
- Final velocity [tex]\( v_2 \)[/tex] = 0.36 m/s
- Time to travel 0.25 m [tex]\( t_1 \)[/tex] = 1.92 s
- Time to travel 0.50 m [tex]\( t_2 \)[/tex] = 2.61 s

The formula to calculate acceleration [tex]\( a \)[/tex] is given by:

[tex]\[ a = \frac{v_2 - v_1}{t_2 - t_1} \][/tex]

Now, substitute the values into the formula:

[tex]\[ a = \frac{0.36 \text{ m/s} - 0.13 \text{ m/s}}{2.61 \text{ s} - 1.92 \text{ s}} \][/tex]

Calculate the numerator (change in velocity):

[tex]\[ 0.36 \text{ m/s} - 0.13 \text{ m/s} = 0.23 \text{ m/s} \][/tex]

Calculate the denominator (change in time):

[tex]\[ 2.61 \text{ s} - 1.92 \text{ s} = 0.69 \text{ s} \][/tex]

Now, divide the change in velocity by the change in time:

[tex]\[ a = \frac{0.23 \text{ m/s}}{0.69 \text{ s}} \approx 0.3333 \text{ m/s}^2 \][/tex]

Thus, the acceleration of the car with two washers added to the string is approximately 0.3333 m/s².