KinematicsMedium
Question
A particle moves along x - axis according to the law x = (t3 - 3t2 - 9t + 5) m. Then :-
Options
A.In the interval 3 < t < 5, the particle is moving in + x direction
B.The particle reverses its direction of motion twice in twice motion if it starts at t = 0
C.The average acceleration from 1≤ t ≤ 2 seconds is 6m / s2
D.In the interval 5 < t < 6 seconds, the distance traveled is equal to the displacement
Solution
x = t3- 3t2 - 9t + 5. x(5) > and x(3) > 0
so [A] v = dx/dt = 3t2 - 6t - 9
⇒ t = - 1, 3 so t = 3
Hence particle reverses its direction only once average acc. = change in velocity / time.
In interval (t = 3 to t = 6), particle does not reverse its velocity and also moves in a straight line so distance = displacement.
so [A] v = dx/dt = 3t2 - 6t - 9
⇒ t = - 1, 3 so t = 3
Hence particle reverses its direction only once average acc. = change in velocity / time.
In interval (t = 3 to t = 6), particle does not reverse its velocity and also moves in a straight line so distance = displacement.
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