No, the equations for final velocity and final speed are not the same. While both concepts relate to the final state of motion, they differ in their definitions.
Final velocity refers to the velocity of an object at the end of a specific time interval or at a particular point in time. It is a vector quantity, which means it has both magnitude (speed) and direction. The equation for final velocity can be derived using the equation of motion:
$v_{f}=v_{i}+at$
Where:
- $v_{f}$ represents the final velocity
- $v_{i}$ represents the initial velocity
- $a$ represents the acceleration of the object
- $t$ represents the time interval
On the other hand, final speed refers to the magnitude of the final velocity, disregarding the direction. It is a scalar quantity, representing only the numerical value. The equation for final speed is derived by ignoring the direction component of the final velocity:
$v_{final speed}=∣v_{f}∣$
In this equation, $∣v_{f}∣$ denotes the magnitude (absolute value) of the final velocity vector.
Therefore, the equations for final velocity and final speed differ in terms of their vector nature. The final velocity accounts for both magnitude and direction, while the final speed only considers the magnitude.