A body starts from rest with uniform accelera | vedclass

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

Question

(D) Given that the body starts from rest,initial velocity $u = 0$.Let the uniform acceleration be $a$.After $n$ seconds,the velocity is $\upsilon = u

Vedclass · Accepted Answer

$\frac{2\upsilon(n - 1)}{n}$

Vedclass · Answer

(D) Given that the body starts from rest,initial velocity $u = 0$.Let the uniform acceleration be $a$.After $n$ seconds,the velocity is $\upsilon = u + an = 0 + an$,so $a = \frac{\upsilon}{n}$.The displacement in $n$ seconds is $S_n = \frac{1}{2}an^2$.The displacement in $(n - 2)$ seconds is $S_{n-2} = \frac{1}{2}a(n - 2)^2$.The displacement in the last two seconds is $\Delta S = S_n - S_{n-2}$.$\Delta S = \frac{1}{2}an^2 - \frac{1}{2}a(n - 2)^2 = \frac{a}{2}[n^2 - (n - 2)^2]$.Using the identity $x^2 - y^2 = (x - y)(x + y)$:$\Delta S = \frac{a}{2}[n - (n - 2)][n + (n - 2)] = \frac{a}{2}[2][2n - 2] = a(2n - 2)$.Substituting $a = \frac{\upsilon}{n}$:$\Delta S = \frac{\upsilon}{n}(2n - 2) = \frac{2\upsilon(n - 1)}{n}$.

$A$ body starts from rest with uniform acceleration. If its velocity after $n$ seconds is $\upsilon$,then its displacement in the last two seconds is

Similar Questions

$A$ bus moving along a straight highway with a speed of $72 \,km/h$ is brought to a halt within $4 \,s$ after applying the brakes. The distance travelled by the bus during this time (assume the retardation is uniform) is . . . . . . $m$.

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion? (in $cm$)

The initial velocity of the particle is $10 \ m/s$ and its retardation is $2 \ m/s^2$. The distance moved by the particle in the $5^{th}$ second of its motion is .......... $m$.

$A$ particle initially at rest is moving along a straight line with an acceleration of $2 \,m/s^2$. At a time of $3 \,s$ after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion in which the particle returns to its initial position is

$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. How long (in $seconds$) does it take for the car to stop?

Vedclass Test Series

Exam Paper Generator

Online Exam Module