Question

How can we find the final position of a body after certain time if we know the initial velocity and the final velocity of that body?

Answer 1

To find the final position of a body after a certain time, given the initial velocity and final velocity, you would need additional information, such as the acceleration or time elapsed during the motion.

If you have the acceleration (assuming it is constant), along with the initial velocity, final velocity, and time elapsed, you can use the following equation:

$\text{Final position}=\text{Initial position}+\left(\frac{\text{Initial velocity}+\text{Final velocity}}{2}\right)\times \text{Time}$

This equation is derived from the kinematic equation for linear motion:

$\text{Final position}=\text{Initial position}+\text{Initial velocity}\times \text{Time}+\frac{1}{2}\times \text{Acceleration}\times {\text{Time}}^2$

However, in the case where acceleration is constant and time is not given, but the initial and final velocities are known, you cannot determine the final position accurately without additional information.

To calculate the final position accurately, you would need at least one of the following:

1. Time: If you know the time elapsed during the motion, you can use the equation above to calculate the final position.

2. Acceleration: If you know the acceleration, you can use kinematic equations to determine the final position. For example, you can use the equation:

Final position=Initial position+Initial velocity×Time+12×Acceleration×Time2 ext{Final position} = ext{Initial position} + ext{Initial velocity} imes ext{Time} + frac{1}{2} imes ext{Acceleration} imes ext{Time}^2Final position=Initial position+Initial velocity×Time+21​×Acceleration×Time<span style="t