Embibe Experts Solutions for Chapter: Rectilinear Motion, Exercise 1: Exercise 1

A particle is moving in $x-y$ plane along curve, $y=\frac{x}{2}$ and $u_{\mathrm{x}}=4-2t.$ The displacement verses time graph of the particle would be (where all parameters are in $\mathrm{S}.\mathrm{I}.$ units)

The acceleration-displacement graph of a particle moving in a straight line is as shown in the figure, the initial velocity of the particle is zero. Find velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the particle when the displacement of the particle is, $s=16 \mathrm{m}.$

A stone is projected at an angle $45°$ with horizontal above horizontal $x$-axis as shown in figure-$1$ (and $y$-axis is vertical). Four graphs representing the magnitude of horizontal $\left(v_{\mathrm{x}}\right)$ or magnitude of vertical $\left(v_{\mathrm{y}}\right)$ component of velocity of stone with respect to time $t$ are as shown. Then which of the following magnitude of velocity versus time graph best represents $v_{\mathrm{y}}$ versus $t$ and $v_x$ versus $t$, respectively for the stone.

(I) 

(II) 

(III) 

(IV)  

A particle is moving along a straight line whose velocity displacement graph is shown. What is the acceleration when displacement is $2 \mathrm{m}$.

The graph shows the variation of velocity of a rocket with time. The maximum height attained by the rocket is

The position-time graph of a moving particle is shown. Then which of the below best represents its velocity-time graph $\left({\mathrm{\theta }}_1={\mathrm{\theta }}_2=120°\right)$

The initial velocity of a particle is given by $u$ (at $t=0$) and the acceleration by $f\text{,}$ where $f=at$  (here $t$ is time and $a$ is constant). Which of the following relation is valid?

A student determined to test the law of gravity for himself walks off a skyscraper $320 \mathrm{m}$ high with a stopwatch in hand and starts his free fall (zero initial velocity). $5$ seconds later, superman arrives at the scene and dives off the roof to save the student. What must be superman's initial velocity in order that he catches the student just before reaching the ground? [Assume that the superman's acceleration is that of any freely falling body $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.