B M Sharma Solutions for Chapter: Kinematics I, Exercise 74: Archives

A particle has an initial velocity $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and an acceleration of $0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}$. Its speed after $10 \mathrm{s}$ is,

A particle is moving with velocity $\overrightarrow{v}=K( y\hat{\mathrm{i}}+x\hat{\mathrm{j}})$, where $K$ is a constant. The general equation for its path is

An object moving with a speed of $6.25 \mathrm{m} {\mathrm{s}}^{-1}$ is decelerated at a rate given by, $\frac{\mathrm{d}v}{\mathrm{d}t}=-2.5\sqrt{v}$
where $v$ is instantaneous speed. The time taken by the object to come to rest would be,

A boy threw a stone up to a maximum height of $10 \mathrm{m}$. The maximum horizontal distance that the boy can throw the stone will be,

Two stones are thrown up simultaneously from the edge of a cliff $240 \mathrm{m}$ high with initial speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ and $40 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. Which of the following graphs best represent the time variation of relative position of the second stone with respect to the first? (Assume that the stones do not rebound after hitting the ground and neglect air resistance. Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. The figures are schematic and not drawn to scale.)

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A rocket is moving in a gravity-free space with a constant acceleration of $2{ \mathrm{m} \mathrm{s}}^{-2}$ along $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \mathrm{m}$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3{ \mathrm{m} \mathrm{s}}^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2{ \mathrm{m} \mathrm{s}}^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is