The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(a + \frac{{{b^2}}}{{3c}}\)

Step-by-step Solution

Detailed explanation

\(\begin{array}{l}
X = at + b{t^2} - c{t^3}\\
V = \frac{{dx}}{{dt}} = a + 2bt - 3c{t^2}\\
a = \frac{{dv}}{{dt}} = 2b - 6ct\\
Put\,acceleration\, = 0\\
\Rightarrow \,\,t = \frac{b}{{3c}}\\
Find\,V\,at\,t = \frac{b}{{3c}}\\
V = \,a + \frac{{{b^2}}}{{3c}}
\end{array}\)

Same subject

A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.

JEE Mains 2026 Medium
The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of :

JEE Mains 2025 Medium
Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be

JEE Mains 2019 Hard
A small bulb is placed at the bottom of a tank containing water to a depth of \(\sqrt{7} \; m\). The refractive index of water is \(\frac{4}{3}\). The area of the surface of water through which light from the bulb can emerge out is \(x \,\pi m ^{2}\). The value of \(x\) is ...............

JEE Mains 2022 Medium
The expression given below shows the variation of velocity \((v)\) with time (t), \(v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}\). The dimension of ABC is :

JEE Mains 2025 Hard
With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength \(5890\) \(\stackrel{\circ}{{A}}\) is observed at \(5896\) \(\stackrel{\circ}{{A}}\) ? (in \({km} / {sec}\))

JEE Mains 2021 Medium

Explore more questions on app

From JEE Mains

When \(100\,g\) of a liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of a liquid \(B\) at temperature \(75\,^oC\), the temperature of the mixture becomes \(90\,^oC\). The temperature of the mixture, if \(100\,g\) of liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of liquid \(B\) at \(50\,^oC\), will be ........\(^oC\)

JEE Mains 2019 Hard
In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

JEE Mains 2021 Medium
Two forces having magnitude \(A\) and \(\frac{ A }{2}\) are perpendicular to each other. The magnitude of their resultant is

JEE Mains 2023 Easy
If a body of mass \(1\) kg falls on the earth from infinity, it attains velocity \((v)\) and kinetic energy \((k)\) on reaching the surface of earth. The values of \(v\) and \(k\) respectively are _______. (Take radius of earth to be \(6400\) km and \(g = 9.8\) m/s\(^2\))

JEE Mains 2026 Medium
A body is projected from the ground at an angle of \(45^{\circ}\) with the horizontal. Its velocity after \(2s\) is \(20 \,ms ^{-1}\). The maximum height reached by the body during its motion is \(m\). (use \(g =10\, ms ^{-2}\) )

JEE Mains 2022 Hard

Explore more questions on app