Kinematics: Solving For Final Velocity Using The Vxf² = Vxi² + 2Ax(∆X) Equation

vxf² = vxi² + 2ax(∆x)

velocity as a function of position

The equation vxf² = vxi² + 2ax(∆x) represents the relationship between the final velocity (vxf), initial velocity (vxi), acceleration (a), and displacement (∆x) of a moving object. This equation is derived from the kinematic equations of motion that describe the motion of an object in a straight line.

Here’s how to understand and use this equation:

– Initial Velocity (vxi): This is the velocity of the object at the start of the time interval being considered.
– Final Velocity (vxf): This is the velocity of the object at the end of the time interval being considered.
– Acceleration (a): This is the rate at which the velocity of the object changes per unit of time. It’s measured in meters per second squared (m/s²).
– Displacement (∆x): This is the change in position of the object during the time interval being considered.

Using this equation, we can solve for any of the four variables if we know the other three. For example, if we know the initial velocity, the acceleration, and the displacement of an object, we can use this equation to find its final velocity at the end of the displacement.

Let’s go through an example to show how to use this equation:

Example: A car starts from rest and accelerates at a rate of 3 m/s² for a distance of 50 meters. What is the final velocity of the car at the end of the displacement?

Given:
– Initial velocity (vxi) = 0 m/s (the car starts from rest)
– Acceleration (a) = 3 m/s²
– Displacement (∆x) = 50 m

To find the final velocity (vxf), we can use the equation:

vxf² = vxi² + 2ax(∆x)

Substituting the values in the equation, we get:

vxf² = (0 m/s)² + 2(3 m/s²)(50 m)
vxf² = 300 m²/s²

Taking the square root of both sides of the equation, we get:

vxf = √300 m/s = 17.3 m/s (rounded to one decimal place)

Therefore, the final velocity of the car at the end of the displacement is 17.3 m/s.

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