(B) The distance between the two particles is given by $s = s_1 - s_2$,where $s_1 = ut$ and $s_2 = \frac{1}{2}ft^2$.$s = ut - \frac{1}{2}ft^2$.To find

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(B) The distance between the two particles is given by $s = s_1 - s_2$,where $s_1 = ut$ and $s_2 = \frac{1}{2}ft^2$.$s = ut - \frac{1}{2}ft^2$.To find the maximum distance,we differentiate $s$ with respect to $t$ and set it to zero:$\frac{ds}{dt} = u - ft = 0 \implies t = \frac{u}{f}$.At this time $t = \frac{u}{f}$,the velocity of the second particle equals the velocity of the first particle.Substituting $t = \frac{u}{f}$ into the expression for $s$:$s_{\max} = u(\frac{u}{f}) - \frac{1}{2}f(\frac{u}{f})^2$$s_{\max} = \frac{u^2}{f} - \frac{u^2}{2f} = \frac{u^2}{2f}$.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Difficult

Two points move in the same straight line starting at the same moment from the same point. The first moves with constant velocity $u$ and the second with constant acceleration $f$. During the time that elapses before the second catches the first,the greatest distance between the particles is $........$

A
$\frac{u}{f}$
B
$\frac{u^2}{2 f}$
C
$\frac{f}{2 u^2}$
D
$\frac{f}{u^2}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in Straight Line

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Uniformly Accelerated Motion

$A$ particle starts from the origin at time $t=0$ and moves in the positive $x$-direction. Its velocity $v$ varies with time as $v=10t \text{ cm/s}$. The distance covered by the particle in $8 \text{ s}$ will be: (in $\text{ cm}$)

EasyTS EAMCET 2018

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If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \ m/s$ to a value approaching zero at $s=30 \ m$,then the acceleration of the particle at $s=15 \ m$ is $........$

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If the engine of a long train moving with constant acceleration crosses a tree with velocity $u$ and the last compartment of the train crosses the same tree with velocity $v$,then the velocity with which the middle compartment crosses the same tree is

DifficultAP EAMCET 2023

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$A$ particle starts with an initial velocity of $10.0 \, m/s$ along the $x$-direction and accelerates uniformly at the rate of $2.0 \, m/s^2$. The time taken by the particle to reach the velocity of $60.0 \, m/s$ is $....... \, s$.

EasyJEE MAIN 2023

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The motion of a body is given by the equation $\frac{dv(t)}{dt} = 6.0 - 3v(t)$,where $v(t)$ is speed in $m/s$ and $t$ is in $s$. If the body was at rest at $t = 0$,which of the following statements is correct?

DifficultIIT 1995

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$A$ particle starts from the origin at time $t=0$ and moves in the positive $x$-direction. Its velocity $v$ varies with time as $v=10t \text{ cm/s}$. The distance covered by the particle in $8 \text{ s}$ will be: (in $\text{ cm}$)

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20 \ m/s$ to a value approaching zero at $s=30 \ m$,then the acceleration of the particle at $s=15 \ m$ is $........$

If the engine of a long train moving with constant acceleration crosses a tree with velocity $u$ and the last compartment of the train crosses the same tree with velocity $v$,then the velocity with which the middle compartment crosses the same tree is

$A$ particle starts with an initial velocity of $10.0 \, m/s$ along the $x$-direction and accelerates uniformly at the rate of $2.0 \, m/s^2$. The time taken by the particle to reach the velocity of $60.0 \, m/s$ is $....... \, s$.

The motion of a body is given by the equation $\frac{dv(t)}{dt} = 6.0 - 3v(t)$,where $v(t)$ is speed in $m/s$ and $t$ is in $s$. If the body was at rest at $t = 0$,which of the following statements is correct?

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