A student is standing at a distance of 50 , m | vedclass

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

Question

(C) Let the student catch the bus after time $t \, s$. The distance covered by the student is $s_s = ut$.The distance covered by the bus starting from

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Let the student catch the bus after time $t \, s$. The distance covered by the student is $s_s = ut$.The distance covered by the bus starting from rest is $s_b = \frac{1}{2}at^2 = \frac{1}{2}(1)t^2 = \frac{t^2}{2}$.For the student to catch the bus,the total distance covered by the student must equal the initial distance plus the distance covered by the bus:$ut = 50 + \frac{t^2}{2}$.Rearranging for $u$:$u = \frac{50}{t} + \frac{t}{2}$.To find the minimum velocity $u$,we differentiate $u$ with respect to $t$ and set it to zero:$\frac{du}{dt} = -\frac{50}{t^2} + \frac{1}{2} = 0$.Solving for $t$:$\frac{50}{t^2} = \frac{1}{2} \implies t^2 = 100 \implies t = 10 \, s$.Substituting $t = 10 \, s$ back into the equation for $u$:$u = \frac{50}{10} + \frac{10}{2} = 5 + 5 = 10 \, m/s$.

Similar Questions

Train $A$ is moving along two parallel rail tracks towards north with speed $72 \ km/h$ and train $B$ is moving towards south with speed $108 \ km/h$. The velocity of train $B$ with respect to $A$ and the velocity of the ground with respect to $B$ are (in $ms^{-1}$):

$A$ train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains is $x$,what should be the minimum retardation of the train to avoid a collision?

Two balls are projected upward simultaneously with speeds $40 \, m/s$ and $60 \, m/s$. The relative position $(x)$ of the second ball with respect to the first ball at time $t = 5 \, s$ is .......... $m$ [Neglect air resistance].

$A$ ball is dropped from a building of height $45 \, m$. Simultaneously,another ball is thrown up with a speed of $40 \, ms^{-1}$. Calculate the relative speed of the balls as a function of time.

Vedclass Test Series

Exam Paper Generator

Online Exam Module