JEE Main 2021 · PhysicsMultiple choiceSingle correctEasyCalculation

JEE Main 25 July 2021, Shift 2, Physics Q3

Question 3 of 90 in this shift, Physics question 3 of 30, Section A.

The instantaneous velocity of a particle moving in a straight line is given as

v = \alpha t + \beta t^2

, where

\alpha

and

\beta

are constants. The distance travelled by the particle between 1 s and 2 s is :

(1) $3\alpha + 7\beta$
(2) $\frac{3}{2}\alpha + \frac{7}{3}\beta$ Official answer
(3) $\frac{\alpha}{2} + \frac{\beta}{3}$
(4) $\frac{3}{2}\alpha + \frac{7}{2}\beta$

Official answer

Option 2

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

3 Apr 2025, Shift 2 · Q28A particle moves along the $x$ -axis and has its displacement $x$ varying with time t according to the equation:…EasySingle correct
6 Apr 2024, Shift 2 · Q57A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2=1+t^2$ . Its acceleration at any time $t$ …MediumNumerical value
1 Feb 2024, Shift 1 · Q51A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was 16 m right of…EasyNumerical value
15 Apr 2023, Shift 1 · Q38The position of a particle related to time is given by $x = (5t^2 - 4t + 5)\,m$ . The magnitude of velocity of the particle at $t = 2s$ …EasySingle correct
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
25 Jun 2022, Shift 2 · Q32Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by…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
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.