Question

An object starts from rest from its starting position and moves along a straight line in such a way that the acceleration of the object at a distance x from its starting position is equal to , i.e. , for . when x=1, the value of is _________.

Answer 1

The question pertains to the physics of simple harmonic motion, with a focus on acceleration as a function of displacement from the starting position.

Step-by-step explanation:

The question is about the acceleration of an object that starts from rest and moves along a straight line with a specific acceleration profile. The acceleration at a distance x from the starting position is proportional to x, which suggests simple harmonic motion. Using Newton's second law, we understand that the acceleration is given by a(t) = kx/m, which is the formula for simple harmonic motion. At x = 1, the value of a(t) would be k/m if we are to assume k is the constant of proportionality in the expression and m is the mass of the object.

We can use the kinematic equation for objects starting from rest, which is x = xo + vot + 1/2at². With initial velocity vo = 0 and knowing acceleration a, we can determine the displacement x after time t.