Question:
The position x of a particle varies with time, (t) as $x = at^2 - bt^3.$ The acceleration will be zero at time t is equal to
The position x of a particle varies with time, (t) as $x = at^2 - bt^3.$ The acceleration will be zero at time t is equal to
Updated On: May 2, 2024
- $\frac{a}{3b}$
- zero
- $\frac{2a}{3b}$
- $\frac{a}{b}$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Distance $ (x) = at^2- bt^3.$
Therefore velocity $ (v) = \frac{dx}{dt} = \frac{d}{dt} (at^2- bt^3)$
$=2at -3bt^2$ and
acceleration $ = \frac{dv}{dt} = \frac{d}{dt} (2at- 3bt^2) = 2a - 6bt = 0$
or $\, \, t = \frac{2a}{6b} = \frac{a}{3b}.$
Therefore velocity $ (v) = \frac{dx}{dt} = \frac{d}{dt} (at^2- bt^3)$
$=2at -3bt^2$ and
acceleration $ = \frac{dv}{dt} = \frac{d}{dt} (2at- 3bt^2) = 2a - 6bt = 0$
or $\, \, t = \frac{2a}{6b} = \frac{a}{3b}.$
Was this answer helpful?
1
0
Top Questions on Motion in a straight line
- A body of mass \( 5 \, \text{kg} \) is placed on a frictionless inclined plane of angle \( 30^\circ \). What is the component of the weight of the body along the plane?
- MHT CET - 2025
- Physics
- Motion in a straight line
- A 5 kg block is placed on a horizontal surface. A force of 10 N is applied to the block. The coefficient of friction between the block and the surface is 0.2. Find the acceleration of the block.
- MHT CET - 2025
- Physics
- Motion in a straight line
- A projectile is fired with an initial velocity of 20 m/s at an angle of 30\(^\circ\) with the horizontal. Calculate the maximum height reached by the projectile.
- MHT CET - 2025
- Physics
- Motion in a straight line
- A car accelerates uniformly from rest to a velocity of \( 25 \, \text{m/s} \) in \( 10 \, \text{seconds} \). What is the acceleration of the car?
- MHT CET - 2025
- Physics
- Motion in a straight line
- The position of body varies as \[ S = 9t^2 - 6t. \text{ What is the time at which the body becomes at rest?} \]
- KEAM - 2025
- Physics
- Motion in a straight line
View More Questions
Questions Asked in NEET exam
- A photon and an electron (mass \(m\)) have the same energy \(E\). The ratio \( \frac{\lambda_{\text{photon}}}{\lambda_{\text{electron}}} \) of their de Broglie wavelengths is: (\(c\) is the speed of light)
- NEET (UG) - 2025
- Dual nature of radiation and matter
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :
- NEET (UG) - 2025
- Pendulums
- De-Broglie wavelength of an electron orbiting in the \(n = 2\) state of hydrogen atom is close to (Given Bohr radius = 0.052 nm):
- NEET (UG) - 2025
- de broglie hypothesis
- The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(d/2\) and \(d/2\) respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25 K_2\), the value of \(K_2\) is :
- NEET (UG) - 2025
- Capacitors and Capacitance
- A wire of resistance \(R\) is cut into 8 equal pieces. From these pieces, two equivalent resistances are made by adding four of these together in parallel. Then these two are added in series. The net effective resistance of the combination is:
- NEET (UG) - 2025
- Resistance
View More Questions
Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.