What is the acceleration of a car that starts from rest with an initial velocity of 0.02 m/s and uniformly travels for 5.06 seconds covering a distance of 25 meters?

The acceleration of the car can be calculated using the formula:
\\(a = \\frac{2(25 - 0.02 \\cdot 5.06)}{5.06^2}\\)
Simplifying further:
\\(a = \\frac{2(25 - 0.1012)}{25.6036}\\)
\\(a = \\frac{2(24.8988)}{25.6036}\\)
\\(a = \\frac{49.7976}{25.6036}\\)
\\(a \\approx 1.945 \\, \\text{m/s}^2\\)
Therefore, the acceleration of the car, given the provided information, is approximately \\(1.945 \\, \\text{m/s}^2\\).

## Calculation for Acceleration:

The acceleration of an object is defined as the rate of change of velocity. In this scenario, the car starts from rest (initial velocity = 0.02 m/s) and travels uniformly, covering a distance of 25 meters in 5.06 seconds.
To find the acceleration, we use the equation of motion:
\[a = \frac{v_f - v_i}{t}\]
where:
\(a\) = acceleration,
\(v_f\) = final velocity,
\(v_i\) = initial velocity,
\(t\) = time taken.
Given that the car starts from rest, the initial velocity (\(v_i\)) is 0.02 m/s. The distance traveled by the car is 25 meters and the time taken is 5.06 seconds.
Plugging these values into the equation, we get:
\[a = \frac{25 - 0.02 \cdot 5.06}{5.06}\]
Solving further:
\[a = \frac{25 - 0.1012}{5.06}\]
\[a = \frac{24.8988}{5.06}\]
\[a \approx 1.945 \, \text{m/s}^2\]
Therefore, based on the given data, the acceleration of the car is approximately 1.945 m/s². This means that the car is gaining a speed of 1.945 meters per second every second as it travels the distance of 25 meters within 5.06 seconds.