Question

A ball is dropped from a table-top. Air resistance may be ignored. Which row describes the velocity and the acceleration of the ball at point X?

A. Acceleration-constant; velocity-constant
B. Acceleration-constant; velocity-increasing
C. Acceleration-increasing; velocity-constant
D. Acceleration-increasing; velocity-increasing

Answer 1

Hint:We are asked to find about the nature of velocity and acceleration of the ball at point X. First check what are the forces acting on the ball which will accelerate the ball. Then to know about the nature of the velocity of the ball, check the direction of velocity and acceleration. Using these information, select the appropriate answer.

Complete answer:
Given, a ball is dropped from a table top and the air resistance is ignored.We are asked to find the nature of velocity and acceleration of the ball at point X.Let us first analyze the forces acting on the ball.It is said air resistance is ignored so the only force acting on the ball is gravitational force. That is, acceleration of the ball will be acceleration due to gravity which is, \[g = 9.8\,{\text{m}}{{\text{s}}^{{\text{ - 1}}}}\] and is constant.Therefore, acceleration of the ball will be constant.

Now, we check for the velocity of the ball.The ball is moving downwards and acceleration due to gravity is also acting downwards which means the velocity is increasing with time.Therefore, we can say the acceleration of the ball will be constant and the velocity of the ball will be increasing at point X.

Hence, the correct answer is option B.

Note: Remember if the acceleration has the same direction as that of the velocity, then the body is speeding up or velocity is increasing and if the acceleration has direction opposite to that of velocity then the body is slowing down or the velocity is decreasing. When the body slows down or the velocity decreases with time then it is known as retardation.