Two points move in the same straight line sta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\frac{u^2}{2 f}$

Vedclass · Answer

(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}$.

Similar Questions

The distance $x$ covered by a particle in one-dimensional motion varies with time $t$ as $x^{2}=at^{2}+2bt+c$. If the acceleration of the particle depends on $x$ as $x^{-n}$,where $n$ is an integer,the value of $n$ is

The velocity of a car accelerating uniformly increases from $20 \ m/s$ to $80 \ m/s$ while covering a distance of $200 \ m$. The time taken is $.... \ s$.

Two cars leave one after the other and travel with an acceleration of $0.4\, m/s^2$. Two minutes after the departure of the first,the distance between the cars becomes $1.9\, km$. The time interval between the departures of the cars is ........$s$.

If a body starts from rest and travels $120 \,cm$ in the $6^{th}$ second,what is the acceleration in $m/s^2$?

$A$ particle is moving in a straight line with initial velocity $u$ and uniform acceleration $a$. If the sum of the distance travelled in the $t^{\text{th}}$ and $(t+1)^{\text{th}}$ seconds is $100 \text{ cm}$,then its velocity after $t$ seconds,in $\text{cm/s}$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module