Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: Assam CEE 2017

The driver of a bus moving at an speed of $60 \mathrm{km} {\mathrm{hr}}^{-1}$ saw a man at a distance of $52 \mathrm{m}$ from the bus. The driver stopped the car at a distance of $2 \mathrm{m}$ from the man using brake. The time required to stop the bus is

The displacement of a particle moving along a straight line is related to time as $\sqrt{x}=t-3$. The displacement of the particle when its velocity is zero is

M.S. Dhoni hits two cricket balls in the air in a $T-20$ match. Both the balls leave his bat at the same velocity but at different angles of $30°$ and $60°$ respectively. If one ignores air friction and wind velocity, which of the following statements is correct? (Angles are with respect to the horizontal)

The position of a particle as a function of time is given by $\overrightarrow{r}\left(t\right)=A\cos \omega t\hat{\mathrm{i}}+B\sin \omega t\hat{\mathrm{j}}$ where $A$ and $B$ are two real positive constants with $A>B$. The orbit of the particle looks like-

The equation of motion of a body is, $\frac{\mathrm{d}v\left(t\right)}{\mathrm{d}t}=9-3v\left(t\right)$ where, $v\left(t\right)$ is the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) at time $t$ (in second). If the body was at rest at $t=0$, then which of the following is correct?

The initial velocity of a projectile is $\left(2\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are along horizontal and vertical directions, respectively. For $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, the equation of the trajectory will be,

A mobile phone of mass $100 \mathrm{g}$ falls from the hand of a person through the window of a train. The train is accelerating at $1 \mathrm{m} {\mathrm{s}}^{-2}$ and just $20 \mathrm{s}$ have passed since it left the station from standstill. If the window is $2 \mathrm{m}$ above the ground. With what kinetic energy will the phone will hit the ground? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A ball of mass $m$ is thrown upward with a velocity $v$. The air exerts an average resisting force $F$. The velocity with which the ball returns to the thrower is