The equation x=t+3 gives the variation of displacement x with time t for a particle moving along the X-axis. Which of the following is correct for the motion of the particle?
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a
velocity the particle is directly proportional to time
b
velocity of the particle is inversely proportional to time
c
the particle has time varying acceleration
d
the acceleration of the particle is constant
answer is D.
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Detailed Solution
Squaring the equation gives x = t 2+ 6t + 9. On differentiation, v = 2t + 6 and a = 2. First option is a good trap, v = 2t + 2 cannot be interpreted as v ∝ t. Only the acceleration is constant