Kinematics

JEE Main level, single correct, medium

91 of 308

Question 91 of 308

Match Column-I with Column-II : Column-I (x-t graphs) Column-II (v-t graphs) A I B II C III D IV Choose the correct answer from the options given below:

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Answer: (A) A- II B-IV, C-III, D-I

(A) Here, the slope dxdt≥0\dfrac{dx}{dt}\geq 0 is always increasing, and we know that the derivative graph of the parabola is straight line, so the graph of velocity-time is straight line with increasing slope.
(A−II)(A-II)
(B) Here, the slope dxdt<0andatt→∞,dxdt→0\dfrac{dx}{dt}\lt 0andatt\rightarrow \infty ,\dfrac{dx}{dt}\rightarrow 0. As the slope is decreasing with time, so the graph of velocity-time will have negative velocity and positive slope.
(B−IV)(B-IV)
(C) Here, the slope dxdt>0forfirsthalfanddxdt<0forsecondhalf\dfrac{dx}{dt}\gt 0forfirsthalfand\dfrac{dx}{dt}\lt 0forsecondhalf.
As the slope of displacement-time is positive constant in first half and negative constant in second half, so the velocity will be uniform positive and uniform negative value.
(C−III)(C-III)
(D) Here, the slope dxdt=constant\dfrac{dx}{dt}=constant.
As the slope of displacement-time is positive constant, so the velocity will be uniform positive value.
(D−I)(D-I)

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