JEE Main 2022 · PhysicsMultiple choiceSingle correctEasyCalculation

JEE Main 25 June 2022, Shift 2, Physics Q32

Question 32 of 90 in this shift, Physics question 2 of 30, Section A.

Two buses

P

and

Q

start from a point at the same time and move in a straight line and their positions are represented by

X_P(t) = \alpha t + \beta t^2

and

X_Q(t) = ft - t^2

. At what time, both the buses have same velocity ?

(1) $\frac{\alpha - f}{1+\beta}$
(2) $\frac{\alpha + f}{2(\beta - 1)}$
(3) $\frac{\alpha + f}{2(1+\beta)}$
(4) $\frac{f - \alpha}{2(1+\beta)}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Motion in a Straight Line
Topic: Kinematics in 1D
Idea tested: Calculus in Kinematics

Same idea in other shifts

Asked 9× in all

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29 Jul 2022, Shift 1 · Q33If $t = \sqrt{x} + 4$ , then $\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)_{t=4}$ is :EasySingle correct
3 Aug 2021, Shift 1 · Q2For the one-dimensional motion described by $x(t) = t - \sin t$ A. $v(t) < 0$ for all $t > 0$ B. $x(t) > 0$ for all $t > 0$ C. $v(t)$ lies…MediumOther
25 Jul 2021, Shift 2 · Q3The instantaneous velocity of a particle moving in a straight line is given as $v = \alpha t + \beta t^2$ , where $\alpha$ and $\beta$ are…EasySingle correct
17 Mar 2021, Shift 2 · Q11The velocity of a particle is $v=v_0+gt+Ft^2$ . Its position is $x=0$ at $t=0$ ; then its displacement after time (t=1) is :EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.