A student is standing at a distance of 50 ,metres from the bus. A… - Vidyadip

MCQ

A student is standing at a distance of $50\,metres$ from the bus. As soon as the bus begins its motion with an acceleration of $1\,ms^{-2}$, the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is.........$ms^{-1}$

A
$5$
B
$8$
✓
$10$
D
$12 $

✓

Answer

Correct option: C.

$10$

c
(c) Let student will catch the bus after $t \,sec$. So it will cover distance $ut$.

Similarly distance travelled by the bus will be $\frac{1}{2}a{t^2}$ for the given condition

$ut = 50 + \frac{1}{2}a{t^2} = 50 + \frac{{{t^2}}}{2}$ [$a = 1\;m/{s^2}$]

$⇒$ $ u = \frac{{50}}{t} + \frac{t}{2}$

To find the minimum value of $u$

$\frac{{du}}{{dt}} = 0$, so we get $t = 10\sec $, then $u = 10\;m/s$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 2. motion in straight line→2. motion in straight line — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $(\overrightarrow A + \overrightarrow B )\, \times (\overrightarrow A - \overrightarrow B )$ is

Taking into account of the slgnificant figures, what is the value of $9.99\, m -0.0099\, m ?$

Following are the graphs of elastic materials. Which one corresponds to that of brittle material?

When $2 \,\,gms$ of a gas are introduced into an evacuated flask kept at $25\,^0C$ the pressure is found to be one atmosphere. If $3 \,\,gms$ of another gas added to the same flask the pressure becomes $1.5$ atmospheres. The ratio of the molecular weights of these gases will be

If the surface tension of a soap solution is $0.03\, MKS$ units, then the excess of pressure inside a soap bubble of diameter $6 \,mm$ over the atmospheric pressure will be

Reading shown in two extended spring balances, $S_1$ and $S_2$ is $60\,kg$ and $30\,kg$ respectively and lift is accelerating upward with acceleration $10\, m/s^2.$ The mass is stationary with respect to lift. Then the mass of the block will be ......... $kg$.

Two identical flutes produce fundamental nodes of frequency $300\,Hz$ at $27\,^oC.$ If the temperature of air in one flute is increased to $31\,^oC,$ the numbe of the beats heard per second will be

A body weighs $250\,N$ on the surface of the earth. ....... $N$ will it weigh half way down to the centre of the earth .

A $50\,kg$ man with $20\,kg$ load on his head climbs up $20$ steps of $0.25\,m$ height each. The work done in climbing is......$J$

The time period of a satellite of earth is $5\, hours$. If the separation between the centre of earth and the satellite is increased to $4\, times$ the previous value, the new time period will become ....... $h$