The position of an object as a function of time is given by the equation x(t) = asin(bt²+ c). The dimensions of a, b, and c are A) distance, angle, and angle. B) distance, angle/time, and angle. C) distance, angle/time², and angle/time². D) distance, angle/time², and angle. E) angle, angle/time², and angle.

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Quizplus · Accepted Answer

The equation x(t) = asin(bt + c) describes the position of an object, where x is distance. For the sine function to be dimensionally consistent, its argument (bt + c) must be dimensionless, implying b has dimensions of angle/time, making it the angular frequency. The constant c, being added to bt, must also be dimensionless, implying it's an angle. Therefore, a must have the dimension of distance to ensure x(t) has dimensions of distance.

The Position of an Object as a Function of Time