Question

A body is thrown up in a lift with a velocity 5m/s relative to the lift and the time of flight is found to be 0.8sec. The acceleration with which the lift is moving up will be:

Answer 1

Hint: In this question, we will use the equation of motion, which gives us a relation between the acceleration, initial velocity, gravity and time. Further, substituting the given values in the equation, we will get our result. Also, we will study the basics of equations on motion.
Formula used:
$a={\displaystyle \frac{2u-gt}{t}}$

Complete answer:
From the equation of motion, we get the relation between the acceleration, initial velocity, gravity and time, we have:
$a={\displaystyle \frac{2u-gt}{t}}$
Substituting the given values in the above equation, we get:
$a={\displaystyle \frac{2\times 5-10\times 0.8}{0.8}}$
$\Rightarrow a={\displaystyle \frac{10-8}{0.8}}$
$\Rightarrow a={\displaystyle \frac{20}{8}}={\displaystyle \frac{5}{2}}$
$\therefore a=2.5m/s^2$
Therefore, we get the required result of acceleration with which the lift is moving up.

Additional information:
As we know that the equations of motion are equations which describe the behavior of a physical system in terms of its motion as a function of time. Further we can say that these equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. Here, dynamic variables are said to be normally spatial coordinates and time is used, but others are also possible, like momentum components and time.
Now, if we go in history, these equations of motion were discovered by Galileo Galilee but he could not manage to prove it practically that his equations were right or not. Later, Sir Isaac Newton proved these three equations of motion practically and also graphically. So, that is the reason now they are often called Newton’s three equations of motion. These equations tell us about the acceleration, displacement, time, final velocity of an object, initial velocity of an object.

Note:
Here we should remember that the three different equations of motion are used in finding different physical properties of a particle under motion. We should also observe that these equations are only applicable to the classical system not in the quantum system.