JEE Mains · Physics · STD 11 - 2. motion in straight line
A particle is moving in a straight line. The variation of position ' \(x\) ' as a function of time ' \(t\) ' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is _______.
- A \(4 \mathrm{~m} / \mathrm{s}\)
- B \(8 \mathrm{~m} / \mathrm{s}\)
- C \(10 \mathrm{~m} / \mathrm{s}\)
- D \(6 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(B) \(8 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\( x=t^3-6 t^2+20 t+15 \) \( \frac{d x}{d t}=v=3 t^2-12 t+20\) \( \frac{d v}{d t}=a=6 t-12\) When \(\mathrm{a}=0\) \(6 \mathrm{t}-12=0 ; \mathrm{t}=2 \mathrm{sec}\) At \(\mathrm{t}=2 \mathrm{sec}\) \(\mathrm{v}=3(2)^2-12(2)+20\) \(\mathrm{v}=8 \mathrm{~m} / \mathrm{s}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards \(A\). If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' \(-2^{\prime}\) then the radius of curvature of meniscus is :JEE Mains 2025 Hard
- Two forces \(\vec{F}_1\) and \(\vec{F}_2\) are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between \(\vec{F}_1\) and \(\overrightarrow{\mathrm{F}}_2\) is \(\cos ^{-1}\left(\frac{1}{\mathrm{n}}\right)\). The value of \(|\mathrm{n}|\) is __________.JEE Mains 2024 Hard
- One gas of \(n_1\) mole of molecules at temperature \(T_1\), volume \(V_1\), and pressure \(P_1\), and another gas of \(n_2\) mole of molecules at temperature \(T_2\), volume \(V_2\), and pressure \(P_2\), are mixed resulting in pressure \(P\) and volume \(V\) of the mixture. The temperature of the mixture is _____.JEE Mains 2026 Medium
- A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\))JEE Mains 2023 Medium
- A light ray is incident, at an incident angle \(\theta_{1}\), on the system of two plane mirrors \(M_{1}\) and \(M_{2}\) having an inclination angle \(75^{\circ}\) between them (as shown in figure). After reflecting from mirror \(M_{1}\) it gets reflected back by the mirror \(M _{2}\) with an angle of reflection \(30^{\circ}\). The total deviation of the ray will be \(\dots\) degree.
JEE Mains 2022 Medium - In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is \(\frac{7 \lambda}{4}\). The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is _______.JEE Mains 2024 Hard
More PYQs from JEE Mains
- Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A pendulum clock when taken to Mount Everest becomes fast. Reason \(R:\) The value of \(g\) (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given belowJEE Mains 2023 Medium
- Two blocks of masses \(10 \; kg\) and \(30 \; kg\) are placed on the same straight line with coordinates \((0,0) \; cm\) and \(( x , 0) \; cm\) respectively. The block of \(10 \; kg\) is moved on the same line through a distance of \(6 \; cm\) towards the other block. The distance through which the block of \(30 \; kg\) must be moved to keep the position of centre of mass of the system unchanged isJEE Mains 2022 Medium
- The surface tension of a soap solution is \(3.5 \times 10^{-2}\) N/m. The work required to increase the radius of a soap bubble from \(1\) cm to \(2\) cm is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is _____. (\(\pi = 22/7\))JEE Mains 2026 Medium
- Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object:JEE Mains 2023 Medium
- The value of \( \text{cosec}10^{\circ}-\sqrt{3}\ \text{sec}10^{\circ} \) is equal to:JEE Mains 2026 Hard
- If the least and the largest real values of \(\alpha,\) for which the equation \(z+\alpha|z-1|+2 i=0\) \(( z \in C\) and \(i=\sqrt{-1}\) ) has a solution, are \(p\) and \(q\) respectively; then \(4\left( p ^{2}+ q ^{2}\right)\) is equal to ..........JEE Mains 2021 Hard