Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

A stone falls freely under gravity. It covers distance, $d_1$ and, $d_2$ in the first $4$ seconds, and the next, $8$ seconds respectively. The ratio $\frac{d_2}{d_1}$ is

The velocity of a particle moving along the $x$- axis varies as a function of time $t$ as $v\left(t\right)=\left(1-3t^2+2t^3\right) \mathrm{m} {\mathrm{s}}^{-1}$ If its position at $t=0$ is $x=0$ then at $=2 \mathrm{s},$ it's position is

Two cars $A$ and $B$ initially at rest are moving in the same direction with accelerations, $a_1$ and $a_2$ respectively. After a certain time, they achieve velocities $v_1$ and $v_2$ respectively and are separated by a distance of $50 \mathrm{m}.$ If $\left(a_1-a_2\right)=4 \mathrm{m} {\mathrm{s}}^{-2},$ then the quantity $\left(v_1-v_2\right)$ will be

A rocket lifts off from the ground and accelerates upwards at $1 \mathrm{m} {\mathrm{s}}^{-2}$. $20$ seconds after liftoff a piece breaks off from the bottom of the rocket. After breaking off, how much time it takes approximately to reach the ground? (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The y-component of vector $\overrightarrow{A}$ is $+3.0 \mathrm{m}$. If A makes an angle of $30°$ counter-clockwise from the positive $y$- axis, the magnitude of $\overrightarrow{A}$ is (assume $\overrightarrow{A}$ is in $x-y$ plane)

Two bodies were thrown simultaneously from the origin: one straight up and the other, at an angle, $60°$ to the vertical. The initial velocity of each body is equal to $10 \mathrm{m} {\mathrm{s}}^{-1}$ Neglecting the air resistance, the distance between the two bodies after $t=2 \mathrm{s}$ is ($\text{ Use }g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A particle leaves the origin with initial velocity $\overrightarrow{v}=\left(3\hat{\mathrm{i}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and a constant acceleration $\overrightarrow{a}=\left(-1\hat{\mathrm{i}}-0.5\hat{\mathrm{j}}\right)\mathrm{m} {\mathrm{s}}^{-2}$. The position vector of particle, when it reaches its maximum $x$-coordinate, is

A particle is moving in $xy$-plane crosses the origin at time $t=0.$ The equation of motion of the particle is $y=4x^2.$ If the velocity of the particle is $\overrightarrow{v}=(2\hat{\mathrm{i}}+2\hat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$ and acceleration is $\overrightarrow{a}=\left(a\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$, then the magnitude of $a$ is