JEE Mains · Physics · STD 11 - 3.2 motion in plane
The position vector of a particle changes with time according to the relation \(\vec r\left( t \right) = 15{t^2}\hat i + \left( {4 - 20{t^2}} \right)\hat j\). What is the magnitude of the acceleration at \(t = 1\) ?
- A \(40\)
- B \(100\)
- C \(25\)
- D \(50\)
Answer & Solution
Correct Answer
(D) \(50\)
Step-by-step Solution
Detailed explanation
\begin{array}{l} \vec r = \left( {15{t^2}} \right)\hat i + \left( {4 - 20{t^2}} \right)\hat j\\ \vec v = \frac{{d\vec r}}{{dt}} = \left( {30t} \right)\hat i - \left( {40t} \right)\hat j\\ \vec a = \frac{{d\vec v}}{{dt}} = \left( {30} \right)\hat i - \left( {40} \right)\hat j\\…
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
- A rectangles solid box of length \(0.3\, m\) is held horizontally, with one of its sides on the edge of a platform of height \(5\,m\). When released, it slips off the table in a very short time \(= 0.01\, s\), remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to:
JEE Mains 2019 Hard - The refractive index of prism is \(\mu=\sqrt{3}\) and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______ \(^\circ\).JEE Mains 2024 Hard
- A series \(L C R\) circuit has \(L=0.01\,H, R=10\,\Omega\) and \(C =1\,\mu F\) and it is connected to ac voltage of amplitude \(\left( V _{ m }\right) 50\,V\). At frequency \(60 \%\) lower than resonant frequency, the amplitude of current will be approximately \(...............\,mA\)JEE Mains 2022 Hard
- 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
- If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\)JEE Mains 2023 Hard
- A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of \(2 \times 10^5 \mathrm{~ms}^{-1}\). When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is \(x \times 10^4 \mathrm{~N} / \mathrm{C}\). The value of \(x\) is _______ Take the mass of the proton \(=1.6 \times 10^{-27} \mathrm{~kg}\).JEE Mains 2025 Hard
More PYQs from JEE Mains
- The coefficient of \(t^4\) in the expansion of \({\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}\) isJEE Mains 2019 Hard
- Four identical rectangular plates with length, \(l=2\, cm\) and breadth, \(b =\frac{3}{2}\, cm\) are arranged as shown in figure. The equivalent capacitance between \(A\) and \(C\) is \(\frac{ x \varepsilon_{0}}{ d } .\) The value of \(x\) is (Round off to the Nearest Integer)
JEE Mains 2021 Medium - The locus of the mid point of the line segment joining the point \((4,3)\) and the points on the ellipse \(x^{2}+2 y^{2}=4\) is an ellipse with eccentricityJEE Mains 2022 Hard
- In a binomial distribution \(B ( n , p )\), the sum and product of the mean and variance are \(5\) and \(6\) respectively, then find \(6(n+p-q)\) is equal to :-JEE Mains 2023 Hard
- If \((1,5,35),(7,5,5),(1, \lambda, 7)\) and \((2 \lambda, 1,2)\) are coplanar, then the sum of all possible values of \(\lambda\) isJEE Mains 2021 Hard
- A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T . If the resistance of the total circuit is \(2 \Omega\) then the force needed to move the rod towards right with constant speed (v) of \(1.5 m / s\) is _________ N.
JEE Mains 2026 Hard