Final answer:
To calculate the final velocity given initial velocity, acceleration, and displacement, the kinematic equation v^2 = v_0^2 + 2a(s - s_0) is used. The process involves substituting known values into the equation and solving for the final velocity.
Step-by-step explanation:
Calculating Final Velocity in Physics
To compute the final velocity when the initial velocity, acceleration, and displacement are known without the time variable, we use one of the kinematic equations for motion with constant acceleration. The specific equation used is:
v^2 = v_0^2 + 2a(s - s_0)
Where v is the final velocity, v_0 is the initial velocity, a is the acceleration, and (s - s_0) is the displacement (the change in position).
Here's a step-by-step breakdown of the process:
- Start with the known values for initial velocity (v_0), acceleration (a), and displacement (s - s_0).
- Plug these values into the kinematic equation.
- Resolve the equation for v^2, the square of the final velocity.
- Take the square root of the result to find the final velocity (v). Note that you will get both a positive and a negative root, representing possible directions of the velocity.
This calculation does not require the time variable, making it useful when only displacement, initial velocity, and acceleration are known.