Question

Go through each statement below carefully and state if it is true or false with reasons and examples?
A particle moving one-dimensionally
(a) having zero speed at a moment may have non-zero acceleration at that moment.
(b) Having zero speed may have non-zero velocity.
(c) Having a fixed speed and must have a zero acceleration.
(d) Having a positive value of acceleration and must be speeding up.

Answer 1

When a particle is reaching the maximum height, the speed of the particle will become zero. Speed is a scalar quantity whereas velocity is a vector quantity which is having both direction as well as magnitude. This all will help you in answering the question.

Complete step by step answer:
(a) If a particle is vertically thrown up in the air, its speed will become zero at maximum height. Even though it will be having an acceleration equal to the acceleration due to gravity that felt in the downward direction at that point. Therefore the first statement is true.
(b) Speed is defined as the magnitude of velocity. When the speed is zero, then the magnitude of velocity will also be zero. Therefore it is false.
(c) Speed is defined as the magnitude of velocity. Fixed speed does not imply a fixed velocity as direction variation may occur. An example for this is uniform circular motion of a particle about a centre. In such situations, acceleration will not be zero. Hence the statement is false.
(d) This statement is not true if the acceleration is positive and velocity is negative at the moment time taken as origin. Therefore, for every time before velocity becomes zero, there will be a slowing down of the particle. When a particle is projected upwards this may happen. Therefore it is an example for the situation. This statement is true when both the velocity and acceleration are positive, at the moment time taken as origin. If a particle is moving with positive acceleration or falling vertically downwards from a height, this may occur.

Note: The acceleration is defined as the rate of variation of velocity with respect to the time. The velocity is defined as the rate of variation of the displacement with respect to time taken. One dimensional motion will be having only one coordinate for expressing the position of the particle.