Embibe Experts Solutions for Chapter: Kinematics, Exercise 3: Exercise - 3

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

A water fountain on the ground sprinkles water all around it. If the speed of the water coming out of the fountain is $v$, the total area around the fountain that gets wet is

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,

A projectile is given an initial velocity of $\hat{\mathrm{i}}+2\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1},$ where $\hat{i}$ is along the ground and $\hat{\mathrm{j}}$ is along the vertical. If $g=10 \mathrm{m} {\mathrm{s}}^{-2},$ the equation of its trajectory is

A particle is moving with speed $v=b\sqrt{x}$ along the positive $x$-axis. Calculate the speed of the particle at time $t=\tau$ (assume that the particle is at the origin at $t=0$).

Consider a body of mass $1.0 \mathrm{kg}$ at rest at the origin at time $t=0.$ A force $\overrightarrow{F}=\left(\alpha t\hat{\mathrm{i}}+\beta \hat{\mathrm{j}}\right)$is applied on the body, where $\mathrm{\alpha }=1.0 {\mathrm{Ns}}^{-1} \mathrm{and} \mathrm{\beta }=1.0 \mathrm{N}.$The torque acting on the body about the origin at time $t=1.0 \mathrm{s}$ is $\overrightarrow{\mathrm{\tau }}$ . Which of the following statements is (are) true?

Small particle of mass $m$ is projected at an angle $\theta$ with the $x-$axis with an initial velocity $v_0$ in the $x-y$ plane as shown in the figure. At a time $t<\frac{v_0\mathrm{sin\theta }}{g}$ the angular momentum of the particle is

where $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along $x,y$ and $z-$ axis respectively.