(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 a 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 a Straight Line

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Uniformly Accelerated Motion

$A$ vehicle starts from rest and accelerates along a straight path at $2 \,m/s^2$. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at $94 \%$ of its original frequency when the vehicle was at rest (in $\,m$)? (Speed of sound $= 330 \,m/s$)

MediumMHT CET 2025

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The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

EasyTS EAMCET 2015

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$A$ particle moves along a straight line. Its position at any instant is given by $x = 32t - \frac{8t^3}{3}$,where $x$ is in $m$ and $t$ is in $s$. Find the acceleration of the particle at the instant when the particle is at rest $..........\,m/s^2$.

Medium

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$A$ particle starts moving rectilinearly at time $t = 0$ such that its velocity $v$ changes with time $t$ according to the equation $v = t^2 - t$,where $t$ is in seconds and $v$ is in $m/s$. The time interval for which the particle retards is

Difficult

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$A$ $100\, m$ long train is moving with a uniform velocity of $45\, km/hr$. The time taken by the train to cross a bridge of length $1\, km$ is.........$s$

Medium

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The displacement of a particle moving in a straight line is given by the expression $x = A t^3 + B t^2 + C t + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

$A$ particle moves along a straight line. Its position at any instant is given by $x = 32t - \frac{8t^3}{3}$,where $x$ is in $m$ and $t$ is in $s$. Find the acceleration of the particle at the instant when the particle is at rest $..........\,m/s^2$.

$A$ particle starts moving rectilinearly at time $t = 0$ such that its velocity $v$ changes with time $t$ according to the equation $v = t^2 - t$,where $t$ is in seconds and $v$ is in $m/s$. The time interval for which the particle retards is

$A$ $100\, m$ long train is moving with a uniform velocity of $45\, km/hr$. The time taken by the train to cross a bridge of length $1\, km$ is.........$s$

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