The six equations below tell us the position in meters as a function of time in seconds for six objects that are moving along a straight line. as the equations show, these objects vary in their initial positions, initial velocities, and accelerations. (a) x(t) = −7 + 9t − 2t2 (b) x(t) = +4 + 9t + t2 (c) x(t) = +3 - 7t - 2t2 (d) x(t) = -4 + 3t - 4t2 (e) x(t) = -1 - 9t - 2t2 (f) x(t) = -7 + t + 2t2
a) which of these objects have a net force acting on them? b) rank the objects based on the magnitude of the net force on them.

a) All of the objects are subjected to a definite net force.

b) D>A=C=E=F>B

Explanation:

Equation of position of the objects as a function of time for the six objects are as follows:

(A)

(B)

(C)

(D)

(E)

(F)

Differentiate each of them to have velocity as a function of time:

(A)

(B)

(C)

(D)

(E)

(F)

Differentiate each of the velocity functions to have acceleration as a function of time:

(A)

(B)

(C)

(D)

(E)

(F)

(a)

Since all of the objects have a non-zero acceleration therefore we can say that all of the objects are subjected to a definite net force. (According to the Newton's first law of motion any body continues to be in the state of rest or in uniform motion until acted upon by any external force.)

(b)

So, according to the magnitude of acceleration, we have the ranking as:

D>A=C=E=F>B

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