Which equation correctly calculates the acceleration of a hamster increasing its velocity from rest to 10m/s in 2s?

The correct choice utilizes the formula for acceleration, which is defined as the change in velocity divided by the time taken for that change. In this scenario, the hamster starts from rest and increases its velocity to 10 m/s in 2 seconds.

To calculate the acceleration, the change in velocity (Δv) is 10 m/s, as the final velocity is 10 m/s and the initial velocity is 0 m/s. The time taken (t) for this change is 2 seconds.

According to the formula for acceleration:

[ a = \frac{Δv}{t} = \frac{10 , \text{m/s}}{2 , \text{s}} ]

This leads to an acceleration calculation of:

[ a = 5 , \text{m/s}^2 ]

This equation correctly captures the relationship between the change in velocity and the time over which that change occurs.

The other choices do not accurately represent the calculation of acceleration based on the fundamental definition. Some involve incorrect mathematical operations or variables that do not align with the definition of acceleration. Therefore, the first option is the only one that correctly applies the formula and leads to the right conclusion.