The position-time (x-t) graph for positive ac | vedclass

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(A) For an object moving with constant positive acceleration $(a > 0)$,the position-time equation is given by the kinematic equation: $x(t) = x_0 + v_

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(A) For an object moving with constant positive acceleration $(a > 0)$,the position-time equation is given by the kinematic equation: $x(t) = x_0 + v_0 t + \frac{1}{2} a t^2$.If we assume the initial position $x_0 = 0$ and initial velocity $v_0 = 0$,the equation simplifies to $x = \frac{1}{2} a t^2$.This equation represents a parabola opening upwards in the $x-t$ plane.As $t$ increases,the slope of the tangent to the curve (which represents velocity $v = \frac{dx}{dt} = at$) also increases,indicating that the velocity is increasing over time,which is the definition of positive acceleration.Therefore,the graph shown in option $A$ represents motion with positive acceleration.

The position-time $(x-t)$ graph for positive acceleration is

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