Motion in a Straight Line
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Question : 11
Total: 27
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) 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.
Solution:
(a) True, when a body is thrown vertically upwards in the space,then at the highest point, the body has zero speed but has downwardacceleration equal to the acceleration due to gravity.
(b) False, because velocity is the speed of body in a given direction.When speed is zero, the magnitude of velocity of body is zero, hencevelocity is zero.
(c) True, when a particle is moving along a straight line with a constantspeed, its velocity remains constant with time. Therefore, acceleration (=change in velocity/time) is zero.
(d) The statement depends upon the choice of the instant of time takenas origin, when the body is moving along a straight line with positiveacceleration. The velocity of the body at an instant of time t is
v = u + a t
The given statement is not correct if a is positive and u is negative, atthe instant of time taken as origin. Then for all the times before the timefor which v vanishes, there is slowing down of the particle i.e. the speedof the particle keeps on decreasing with time. It happens when body isprojected vertically upwards. However the given statement is true if uis positive and a is positive, at the instant of time taken as origin. It is sowhen the body is falling vertically downwards.
(b) False, because velocity is the speed of body in a given direction.When speed is zero, the magnitude of velocity of body is zero, hencevelocity is zero.
(c) True, when a particle is moving along a straight line with a constantspeed, its velocity remains constant with time. Therefore, acceleration (=change in velocity/time) is zero.
(d) The statement depends upon the choice of the instant of time takenas origin, when the body is moving along a straight line with positiveacceleration. The velocity of the body at an instant of time t is
The given statement is not correct if a is positive and u is negative, atthe instant of time taken as origin. Then for all the times before the timefor which v vanishes, there is slowing down of the particle i.e. the speedof the particle keeps on decreasing with time. It happens when body isprojected vertically upwards. However the given statement is true if uis positive and a is positive, at the instant of time taken as origin. It is sowhen the body is falling vertically downwards.
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