Question:
Displacement x versus $t^2$ graph is shown for a particle. The acceleration of the particle is :
Displacement x versus $t^2$ graph is shown for a particle. The acceleration of the particle is :
Updated On: May 19, 2022
- $2\,m/s^2$
- $4\,m/s^2$
- $8\,m/s^2$
- zero
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
From graph,
x = Slope $\left(t^{2}\right) $
$x =\frac{2-0}{1-0}\left(t^{2}\right) $
$x =2 t^{2} $
$\frac{d x}{d t} =4 t $
$\frac{d^{2} x}{d t^{2}} =4$
$a =4 \,m / s ^{2}$
$[\because \frac{d^{2} X}{d t^{2}}=a]$
x = Slope $\left(t^{2}\right) $
$x =\frac{2-0}{1-0}\left(t^{2}\right) $
$x =2 t^{2} $
$\frac{d x}{d t} =4 t $
$\frac{d^{2} x}{d t^{2}} =4$
$a =4 \,m / s ^{2}$
$[\because \frac{d^{2} X}{d t^{2}}=a]$
Was this answer helpful?
0
0
Top Questions on Acceleration
- A uniform solid cylinder of mass \( m \) and radius \( r \) rolls along an inclined rough plane of inclination \( 45^\circ \). If it starts to roll from rest from the top of the plane, then the linear acceleration of the cylinder axis will be:
- JEE Main - 2025
- Physics
- Acceleration
- A particle moves in a circle of radius 2 m with a speed of 6 m/s. What is the centripetal acceleration of the particle?
- BITSAT - 2025
- Physics
- Acceleration
- The acceleration of a particle varies with time as \( a = 6t \). What is the displacement and velocity of the particle at \( t = 4s \)?
- KEAM - 2025
- Physics
- Acceleration
- A balloon and its content having mass \( M \) is moving up with an acceleration \( a \). The mass that must be released from the content so that the balloon starts moving up with an acceleration \( 3a \) will be:
- JEE Main - 2025
- Physics
- Acceleration
- The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:
- JEE Main - 2024
- Physics
- Acceleration
View More Questions
Questions Asked in UPSEE exam
- Which of the following carbohydrates are branched polymer of glucose
- UPSEE - 2019
- Carbohydrates
- The imaginary part of $\left( \frac{1}{2} + \frac{1}{2}i\right)^{10} $ is
- UPSEE - 2019
- Complex Numbers and Quadratic Equations
Acetic acid dissociates 1.3%. What will be the pH of \(\frac {N}{10}\) solution of the acid.
- UPSEE - 2019
- Acids and Bases
Let z = x + iy be a complex number satisfying the following equation |z - (2 + i)| = |Re(z) - 4 | Which of the following options describes the above equation?
- UPSEE - 2019
- Complex Numbers and Quadratic Equations
- Let z = x + iy be a complex number. The equation arg $\left( \frac{z + 1}{z}\right) = \frac{\pi}{4}$ represents
- UPSEE - 2019
- Complex Numbers and Quadratic Equations
View More Questions
Concepts Used:
Acceleration
In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
