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Given :
Find the time instants when the particle is at origin of reference and initial position. Also find the time when velocity is zero.
The position of the particle with respect to origin of reference is given by :
In order to determine time instants when the particle is at origin of reference, we put x=0,
In order to determine time instant when particle is at initial position, we put x=10,
The particle is at the initial position twice, including start of motion. Now, at the point of reveral of direction, speed of the particle is zero. Putting v = 0 and using v=u+at,
Case 2: Initial position and origin of reference are different. Initial position is positive. Initial velocity is positive i.e. it is directed in reference direction. The velocity and acceleration are in same direction.
The particle is accelerated so long force causing acceleration is applied on the particle. The segement AF with origin at D is typical graph of free fall of particle under gravity, considering AF as the height of fall and downward direction as positive direction. Only differing aspect is that particle has initial velocity. Neverthless, the nature of curve of free fall is similar. Note that speed of the particle keeps increasing till it hits the ground.
Given
Find the time instants when the particle is at origin of reference and initial position. Also find the time when velocity is zero.
The position of the particle with respect to origin of reference is given by :
In order to determine time instants when the particle is at origin of reference, we put x=0,
We neglect both these negative values and deduce that the particle never reaches point of origin. In order to determine time instant when particle is at initial position, we put x=10,
We neglect negative value. The particle is at the initial position only at the start of motion. Now, at the point of reveral of direction, speed of the particle is zero. Putting v = 0 and using v=u+at,
The particle never changes its direction.
Case 3: Initial position and origin of reference are same. Initial velocity is negative i.e. it is directed in negative reference direction. The velocity and acceleration are oppositely directed.
Initially particle is decelerated as the speed of the particle keeps on decreasing till it becomes zero at point C. This is indicated by the diminishing slope (magnitude) of the tangents to the curve. Subsequently, particle is accelerated so long force causing accleration is applied on the particle.
Given
Find the time instants when the particle is at origin of reference. Also find the time when velocity is zero.
The position of the particle with respect to origin of reference is given by :
In order to determine time instants when the particle is at origin of reference, we put x=0,
The particle is at the origin of reference twice, including start of motion. Now, at the point of reversal of direction, speed of the particle is zero. Putting v = 0 and using v=u+at,
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