In kinematics, which equation is applicable when acceleration is unknown?

The equation v² = v₀² + 2ax is applicable when acceleration is unknown because it relates the initial speed, final speed, acceleration, and displacement in a way that does not require explicit knowledge of the time variable or direct calculation of acceleration.

In this equation:

• v represents the final velocity,
• v₀ is the initial velocity,
• a is the acceleration, and
• x is the displacement.

This relationship allows one to find the final velocity or displacement without needing the acceleration directly calculated from a known time. As long as you have two of the other variables in the equation, you can solve for the third.

For example, if you know the initial velocity and the displacement, you can rearrange the equation to find the final velocity without needing to know how long it took to travel that distance, or if you know the final velocity and initial velocity with the same displacement, you can find the acceleration.

In contrast, the first equation, which includes acceleration (x = v₀t + ½at²), explicitly requires knowledge of acceleration or time. The second equation (v = v₀ + at) also requires knowledge of acceleration directly. The last equation (x = vt) is only applicable