# For the one-dimensional motion, described by x = t–sintA. x (t) > 0 for all t > 0.B. v (t) > 0 for all t > 0.C. a (t) > 0 for all t > 0.D. v (t) lies between 0 and 2.

Option (a) is correct. For x(t) > 0 for t > 0  Dividing by t on both sides, this wouldn’t affect the inequality, since we have assumed t > 0. This is always true for any t > 0.

Option (b) is incorrect. v(t) = dx/dt = 1 – cos(t) which is equal to zero at t = 2nП

Option (c) is incorrect. a(t) = dv/dt = - sin(t) which can have both positive and negative values.

Option (d) is correct. v(t) = 1 – cos(t). cos(t) lies between 1 and -1, so v(t) lies between 0 and 2 (when cos(t) = 1 and when cos(t) = -1 respectively).

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