Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: AMU-AT (B.Tech.) 2017

Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

Acceleration-time graph of a body moving in a straight line is as shown in figure. The body started its motion from rest.

At which point is the body moving with the largest speed?

The displacement of a body is given by $x=4\mathrm{t}+5{\mathrm{t}}^3,$ where $x$ is in metre and $t$ is in second. The difference between the average velocity of the body in the time-interval $t=1 \mathrm{s}$ to $t=2 \mathrm{s}$ and its instantaneous-velocity at $t=1 \mathrm{s}$ is

The relation between time $t$ and distance $x$ for a moving particle is $t=\alpha x^2+\beta x,$ where $\alpha$ and $\beta$ are constants. If $v$ is the velocity at distance $x$, then the retardation of the particle is

Two seconds after projection, a projectile is moving at $30°$ above the horizontal, after one more second, it is moving horizontally. The initial speed of the projectile is (Take $\left.g=10 {\mathrm{ms}}^{-2}\right)$

A particle has initial velocity $\left(2\hat{i}+3\hat{j}\right)$ and acceleration $\left(0.3\hat{i}+0.2\hat{j}\right)$. The magnitude of velocity after $10$ seconds will be

If a particle's position is given by $x=4-12t+3t^2$ where $t$ is in the seconds and $x$ in meters. What is its velocity at $t=1s$? Whether the particle is moving in positive $x$ direction or negative $x$ direction?

A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{d}{2}$ Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as