(B) The position of the body is given by the equation $x = 4t^2 - 12t$.To find the velocity $v$,we differentiate the position $x$ with respect to time

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(B) The position of the body is given by the equation $x = 4t^2 - 12t$.To find the velocity $v$,we differentiate the position $x$ with respect to time $t$:$v = \frac{dx}{dt} = \frac{d}{dt}(4t^2 - 12t) = 8t - 12 \, m/s$.To find the acceleration $a$,we differentiate the velocity $v$ with respect to time $t$:$a = \frac{dv}{dt} = \frac{d}{dt}(8t - 12) = 8 \, m/s^2$.Therefore,the acceleration of the particle is $8 \, m/s^2$.

Class 11 Physics Motion in a Straight Line Acceleration and its graph

Easy

$A$ body starts from the origin and moves along the $x$-axis such that its position at any instant is $x = 4t^2 - 12t$,where $t$ is in seconds and $x$ is in meters. What is the acceleration of the particle in $m/s^2$?

A
$4$
B
$8$
C
$24$
D
$0$

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Motion in a Straight Line

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Acceleration and its graph

$A$ particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be.....$m/s$.

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Will the acceleration increase or decrease with an increase in velocity?

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The acceleration-time graph is given. If the initial velocity is $5\,m/s$,then the velocity after $2\,s$ is.......$m/s$.

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The displacement is given by $x = 2t^2 + t + 5$,the acceleration at $t = 2 \ s$ is ......... $m/s^2$.

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The position, velocity, and acceleration of a particle moving with a constant acceleration can be represented by which of the following sets of graphs?

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$A$ body starts from the origin and moves along the $x$-axis such that its position at any instant is $x = 4t^2 - 12t$,where $t$ is in seconds and $x$ is in meters. What is the acceleration of the particle in $m/s^2$?

Similar Questions

$A$ particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be.....$m/s$.

Will the acceleration increase or decrease with an increase in velocity?

The acceleration-time graph is given. If the initial velocity is $5\,m/s$,then the velocity after $2\,s$ is.......$m/s$.

The displacement is given by $x = 2t^2 + t + 5$,the acceleration at $t = 2 \ s$ is ......... $m/s^2$.

The position, velocity, and acceleration of a particle moving with a constant acceleration can be represented by which of the following sets of graphs?

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