A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x=c_0(t^2-2)+c (t-2 )^2 where c_0 and c are constants of appropriate dimensions. Then, whic…

Question

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x=c_0(t^2-2)+c (t-2 )^2 where c_0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

Accepted Answer

Correct answer: A. (a) To determine the acceleration of the particle, we start by differentiating the displacement function with respect to time t. The displacement of the particle is given by: x=c_0(t^2-2)+c (t-2 )^2 First, compute the velocity v by differentiating x with respect to t : v= dx dt= d dt(c_0(t^2-2)+c (t-2 )^2) This gives: v=2c_0t+2c (t-2 ) Next, determine the acceleration a by differentiating the velocity function with respect to time t : a= dv dt= d dt(2c_0t+2c (t-2 )) Calculating this gives: a=2c_0+2c Hence, the acceleration of the particle is 2c_0+2c

$A particle moves along the x -axis and has its displacement x varying with time t according to the equation: x = c_{0} (t^{2} - 2) + c (t - 2)^{2} where c_{0} and c are constants of appropriate dimensions. Then, which of the following statements is correct?$

Solution

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