Acceleration in 1D

Q. The figure shows the v - t graph of a particle moving in straight line. Find the time (in $s$) when particle returns to the starting point.

Q. A particle moves along x-axis as x=4(t-2)+a$(t-2{)}^2$ Which of the following is true?

1. The initial velocity of particle is 4
2. The particle is at origin at t = 0
3. None of these
4. The acceleration of particle is 2a

Q. At zero acceleration, a particle moves along a straight line. What is the velocity of a particle at the position of x = $t^4-20t^2+42$?

1. -48.68 m/sec
2. +48.68 m/sec
3. -42 m/sec
4. + 42 m/sec

Q. Starting from the origin at time $t=0$, with initial velocity $5\hat{j}{\text{ms}}^{-1}$, the particle moves in the $x-y$ plane with a constant acceleration of $(10\hat{i}+4\hat{j}){\text{m/s}}^2$. At time $t$, its coordinates are $(20\text{m},y_0\text{m})$. The values of $t$ and $y_0$ are, respectively:

1. $\text{2 s and 18 m}$
2. $\text{4 s and 52 m}$
3. $\text{2 s and 24 m}$
4. $\text{5 s and 25 m}$

Q. The acceleration of a particle is defined by the relation, $a=-4x(-1+\frac{1}{4}{x}^2)$ , where $x$ is displacement along $x-$ axis. All the quantities are in $SI$ units. If velocity of the particle $\left(v\right)=17\text{m/s}$ when $x=0$, then the velocity of the particle when $x=4\text{m}$ is

1. $12\text{m/s}$
2. $15\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$

Q. The velocity of a particle at $t=0$ at origin is $\overrightarrow{u}=4\hat{i}+3\hat{j}\text{m}/sec$ and a constant acceleration is $\overrightarrow{a}=6\hat{i}+4\hat{j}\text{m}/se{c}^2$. Find the displacement of the particle at $t=2sec$

1. $(20\hat{i}+14\hat{j})$ $m$
2. $(20\hat{i}-14\hat{j})$ $m$
3. $(-20\hat{i}+14\hat{j})$ $m$
4. $(-20\hat{i}-14\hat{j})$ $m$

Q. Starting from the origin at time $t=0$, with initial velocity $5\hat{j}{\text{ms}}^{-1},$ a particle moves in the $xy-$ plane with a constant acceleration of $10\hat{i}+4\hat{j}{\text{ms}}^{-2}.$ At time $t$, its coordinates are $20\text{m},y_0\text{m}.$ The values of $t$ and $y_0$ are, respectively-

1. $\text{2 s and 18 m}$
2. $\text{4s and 52 m}$
3. $\text{2 s and 24 m}$
4. $\text{5 s and 25 m}$

Q. A particle moves from the point $(2.0\hat{i}+4.0\hat{j})\text{m}$, at $t=0$, with an initial velocity $(5.0\hat{i}+4.0\hat{j}){\text{ms}}^{-1}$. It is acted upon by a constant force, which produces a constant acceleration of $(4.0\hat{i}+4.0\hat{j}){\text{ms}}^{-2}$. What is the distance of the particle, from the origin, at time $2s$?

1. $5\text{m}$
2. $10\sqrt{2}\text{m}$
3. $20\sqrt{2}\text{m}$
4. $15\text{m}$

Q. A particle is moving along straight line (x axis) & position of particle is given by $x=t^2-7t+12$, then at $t=3.2$, the speed of particle will

1. increase
2. decrease
3. become zero
4. increase or decrease

Q. The acceleration of a particle is defined by the relation, $a=-4x(-1+\frac{1}{4}{x}^2)$ , where $x$ is displacement along $x-$ axis. All the quantities are in $SI$ units. If velocity of the particle $\left(v\right)=17\text{m/s}$ when $x=0$, then the velocity of the particle when $x=4\text{m}$ is

1. $12\text{m/s}$
2. $15\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$

Q. The figure shows the v - t graph of a particle moving in straight line. Find the time (in $s$) when particle returns to the starting point.

Q. The figure shows the v - t graph of a particle moving in straight line. Find the time (in $s$) when particle returns to the starting point.

Q. The figure shows the v - t graph of a particle moving in straight line. Find the time (in $s$) when particle returns to the starting point.

Q. The figure shows the v - t graph of a particle moving in straight line. Find the time (in $s$) when particle returns to the starting point.

Q. The displacement of a body along y-axis is given by, $2y=g{t}^2$ ($g$ is a constant & $t$ is the time taken). What will be the acceleration of the body along y-axis at any time t ?

1. $g$
2. $\frac{1}{2}gt$
3. None of these
4. $2g$

Q. The acceleration of a particle is defined by the relation, $a=-4x(-1+\frac{1}{4}{x}^2)$ , where $x$ is displacement along $x-$ axis. All the quantities are in $SI$ units. If velocity of the particle $\left(v\right)=17\text{m/s}$ when $x=0$, then the velocity of the particle when $x=4\text{m}$ is

1. $12\text{m/s}$
2. $15\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$

Q. The acceleration of a particle is defined by the relation, $a=-4x(-1+\frac{1}{4}{x}^2)$ , where $x$ is displacement along $x-$ axis. All the quantities are in $SI$ units. If velocity of the particle $\left(v\right)=17\text{m/s}$ when $x=0$, then the velocity of the particle when $x=4\text{m}$ is

1. $12\text{m/s}$
2. $15\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$