Question

A particle is thrown up vertically with a speed \[{v_1}\]​ in air. It takes time \[{t_1}\]​ in upwards journey and \[{t_2}\left( { > {t_1}} \right)\] in the downward journey and returns to the starting point with a speed \[{v_2}\]​. Then,
A. \[{v_1} = {v_2}\]
B. \[{v_1} < {v_2}\]
C. \[{v_1} > {v_2}\]
D. Data is insufficient

Answer 1

Hint: Velocity depends on the distance covered by the particle and time taken to cover that distance. In this case, the distance covered by the particle is the same in both the directions which are upward and downward, but the time taken differs in both the cases.
Complete step by step answer:
Given: The time taken to cover the distance in the downward direction is more than the time taken to cover upward.
The velocity of a particle depends directly on the distance covered, which means if the distance covered by the particle increases, then the particle’s velocity also increases. Also, the particle’s velocity depends inversely on the time taken by the particle to cover the distance, which means the velocity of the particle increases when the time taken to cover the distance decreases.
Since the distance covered in both the cases is the same; therefore the distance does not affect the velocity of the particle in either case.
The time taken by the particle in the upward direction is less than the time taken by the particle in the downward direction, therefore the velocity of the particle increases in the upward direction and decreases in the downward direction.

So, the correct answer is “Option 3”.

Note:
The velocity of the particle can also be affected by the acceleration due to gravity. The acceleration of the gravity remains constant at some particular distance from the surface of the earth but decreases if a particle moves far away from the surface of the Earth.