An object starts from rest and slides with negligible friction down an air track tipped at an angle theta from the horizontal. a student records values of the object's position along the track at various times. the value of theta can best be determined from which of the following? the y-intercept of a graph of position as a function of time the y-intercept of a graph of position as a function of the square of time the slope of a graph of position as a function of time the slope of a graph of position as a function of the square of time

The value of theta can best be determined from the slope of a graph of position as a function of the square of time.

Let the angle of inclination of the track, = θ

Let the acceleration of the object = a

Generally, the slope of a graph is given as;

The vertical component of the force on the object along the track is calculated as;

The horizontal component of the force on the object along the track is calculated as;

The coefficient of friction on the object is calculated as;

Thus, the value of theta can best be determined from the slope of a graph of position as a function of the square of time.

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The value of θ can be determined by slope of graph as function of square of time.

Explanation:

Lets take

Mass = m

Angle of inclination =θ

From diagram

mg sinθ = m a

So

a=g sinθ

We know that

Given that block is in rest position initially.

u= 0

We can say that

S∝ t²      If we assume that t and x and S as y y= m x

Here slope ,m

So the value of θ can be determined by slope of graph as function of square of time.

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