Q11 of 28 Page 55

Read each statement below carefully and state with reasons and examples, if it is true or false ;

A particle in one-dimensional motion


(a) with zero speed at an instant may have non-zero acceleration at that instant


(b) with zero speed may have non-zero velocity,


(c) with constant speed must have zero acceleration,


(d) with positive value of acceleration must be speeding up.

(a) True.


Explanation: When an object is vertically thrown upwards, at maximum height its velocity becomes zero. However, its acceleration remains constant (acceleration due to gravity).


(b) False.


Explanation: Speed and velocity have same magnitude for a body. So, If a body is having zero speed it should have zero velocity.


(c) True.


Explanation: Acceleration is defined as change in velocity with respect to time. Thus, If change in velocity is zero acceleration is also zero.


(d) False.


Explanation: When a body is vertically thrown upwards. Even though positive acceleration the body have it will slowly speeding down due acceleration due to gravity.


True.


Explanation: When a body is freely falling from a height. Acceleration due to gravity speedup the body.


More from this chapter

All 28 →
9

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km/h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

 10

A player throws a ball upwards with an initial speed of 29.4 m/s.

(a) What is the direction of acceleration during the upward motion of the ball?


(b) What are the velocity and acceleration of the ball at the highest point of its motion?


(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.


(d) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 ms-2 and neglect air resistance).

 12

A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.

 13

Explain clearly, with examples, the distinction between:

(a) Magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;


(b) Magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first. When is the equality sign true? [For simplicity, consider one-dimensional motion only].