Given the kinematics equation for the motion of an object falling from rest, x=.

Question

Given the kinematics equation for the motion of an object falling from rest, x=.5g*t2), what kind of relationship is predicted between x and t? (select all that apply)

Question options:

(a) x=k*t+b, where k and b are constants.
(b) displacement, x, has a linear relationship with time, t.
(c) displacement, x, and time, t, obey a power law.
(d) x=k*t2, where k is a constant.
(e) displacement, x, is proportional to time, t.
(f) diplacement, x, is proportional to the square of the time, t2.
(g) x=k*t, where k is a constant

Explanation / Answer

From the kinematics relation S = ut + ( 1/ 2) at 2 Where S = displacment u = Initial velocity = 0 Since it fall from rest t = time a = accleration = + g Substitute values we get S = 0 + ( 1/ 2) gt 2 S = ( 1/ 2) gt 2 = k t 2 Where k = constant = g / 2 i.e., diplacement, x, is proportional to the square of the time, t2 hope helps please atleast rate me helpful

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