Introduction to acceleration

Q.

The relation between time $t$ and distance $x$ is $t=\alpha x^2+\beta x$ where $\alpha$ and $\beta$ are constants. The retardation is

1. $-2\alpha v^3$

2. $2\beta v^3$

3. $2\alpha \beta v^3$

4. $2\beta 2v^3$

Q. The acceleration-displacement graph of a partice moving in a straight line is shown in the figure. Initial velocity of the particle is zero. Find the velocity of the particle when displacement of the particle is $12\text{m}$.

1. $3\sqrt{2}\text{m/s}$
2. $2\sqrt{5}\text{m/s}$
3. $4\text{m/s}$
4. $4\sqrt{3}\text{m/s}$

Q. A man loses $20\%$ of his velocity after running through $108\text{m}$. If the rate by which he is losing his velocity remains constant, what is the maximum distance he will cover?

1. $218\text{m}$
2. $300\text{m}$
3. $324\text{m}$
4. $192\text{m}$

Q. The displacement ($s$) of a particle is proportional to the first power of time $t$, i.e., $s\propto t$; then the acceleration of the particle is

1. Infinite
2. Zero
3. A small finite value
4. A large finite value

Q. What is the acceleration, if the body starts from the rest and travels a distance of $s\text{m}$ in $2$ seconds?

1. $\frac{2}{3}s{\text{m/s}}^2$
2. $\frac{3}{2}s{\text{m/s}}^2$
3. $\frac{1}{3}s{\text{m/s}}^2$
4. $\frac{1}{2}s{\text{m/s}}^2$

Q.

What do you mean by positive acceleration?

Q. A bullet fired into a fixed target loses half of its velocity after penetrating $3cm$. How much further will it penetrate before coming to rest assuming that it faces constant resistance to motion?

1. $1.5cm$
2. $1.0cm$
3. $3.0cm$
4. $2.0cm$

Q. The $x$ coordinates of a particle at any time $t$ are given by $x=7t+4t^2$ where $x$ is in $m$ and $t$ in $\text{s}$. The acceleration of the particle at $5\text{s}$ is

1. zero
2. $8{\text{m/s}}^2$
3. $20{\text{m/s}}^2$
4. $40{\text{m/s}}^2$

Q. What is the acceleration, if the body starts from the rest and travels a distance of $s\text{m}$ in $2$ seconds?

1. $\frac{2}{3}s{\text{m/s}}^2$
2. $\frac{3}{2}s{\text{m/s}}^2$
3. $\frac{1}{3}s{\text{m/s}}^2$
4. $\frac{1}{2}s{\text{m/s}}^2$

Q. An object moves velocity $\overrightarrow{v}$ having constant accelaration $\overrightarrow{a}$. Which of the following expressions are variable quantities ?

1. $\frac{d|\overrightarrow{v}|}{dt}$
2. $\left|\frac{d\overrightarrow{v}}{dt}\right|$
3. $\frac{d\left(|\overrightarrow{v}{|}^2\right)}{dt}$
4. $\frac{d\left(\frac{\overrightarrow{v}}{\overrightarrow{|v|}}\right)}{dt}$

Q. A car starting from rest accelerates at the rate $f$ through a distance $s$, then continues at constant speed for time $t$ and then decelerates at rate $\frac{f}{2}$ to come to rest. If the total distance covered is $15s$, then which one is correct?

1. $s=\frac{f{t}^2}{72}$
2. $s=\frac{f{t}^2}{4}$
3. $s=\frac{f{t}^2}{6}$
4. $s=\frac{f{t}^2}{2}$

Q. If velocity of the particle is given by $v=\sqrt{x}$, where $x$ denotes the position of the particle and initially particle was at $x=4$, then which of the following are correct ?

1. At $t=2\text{s}$, the position of the particle is $x=9$
2. Particle's acceleration at $t=2\text{sec}$, is $1{\text{m/s}}^2$
3. Particle's acceleration is $\frac{1}{2}{\text{m/s}}^2$ throughout the motion
4. Particle will never go in negative direction from its starting position

Q. A body starts from orgin and moves along x-axis such that its velocity is $v=(4t^3-2t)$ m/s. Acceleration of particle when it is 2 m from origin is.

1. $10m/s^2$
2. $20m/s^2$
3. $11m/s^2$
4. $22m/s^2$

Q. A sports car can accelerate uniformly to a speed of $162\text{km/h}$ in $5\text{s}$. Its maximum braking retardation is $6{\text{m/s}}^2$. The minimum time in which it can travel $1\text{km}$, starting from rest and ending at rest, in seconds is?

Q. On seeing a speed limit road sign, you apply brakes that bring your car from the speed of $30\text{m/s}$ to a speed of $20\text{m/s}$, covering a distance of $100\text{m}$ at a constant deceleration. How much time is required for the given decrease in speed?

1. $3\text{s}$
2. $4\text{s}$
3. $2\text{s}$
4. $5\text{s}$

Q. The velocity of a body is dependent on its position as $v=\sqrt{x}$, where $v$ and $x$ are in SI units. Then its acceleration

1. increases linearly
2. decreases linearly
3. remains constant
4. first increases and then decreases

Q. A particle is moving along the positive $x$-axis and at $t=0$, the particle is at $x=0$. The acceleration of the particle is a function of time. The acceleration at any time $t$ is given by $a=2(1–[t\left]\right)$ where $\left[t\right]$ is the greatest integer function. Assuming that the particle is at rest initially, the displacement of the particle in $4s$ is

1. $1m$
2. $2m$
3. $6m$
4. $4m$

Q. A body starts from rest with acceleration $2{\text{m/s}}^2$ till it attains the maximum velocity, then retards to rest with $3{\text{m/s}}^2$. If total time taken is $10$ seconds then maximum speed attained is

1. $12\text{m/s}$
2. $8\text{m/s}$
3. $6\text{m/s}$
4. $4\text{m/s}$

Q. A car which has an initial velocity of $4\text{m/s}$ accelerates at the rate of $2{\text{m/s}}^2$ for $5\text{s}$. What will be the distance (in $\text{m}$) that it covers in these $5\text{s}$ ?

Q. A car which has an initial velocity of $4\text{m/s}$ accelerates at the rate of $2{\text{m/s}}^2$ for $5\text{s}$. What will be the distance (in $\text{m}$) that it covers in these $5\text{s}$ ?

Q. The displacement ($s$) of a particle is proportional to the first power of time $t$, i.e., $s\propto t$; then the acceleration of the particle is

1. Infinite
2. Zero
3. A small finite value
4. A large finite value

Q. A particle returns to the starting point after $10\text{s}$. if the rate of change of velocity during the motion is constant, then its location after $7\text{s}$ will be same as that after

1. $3\text{s}$
2. $4\text{s}$
3. $5\text{s}$
4. $6\text{s}$

Q. A car moving with a speed of $50\text{km/h}$ can be stopped by brakes after at least $6\text{m}$. If the same car is moving at a speed of $100\text{km/h}$, the minimum stopping distance is:

1. $12\text{m}$
2. $18\text{m}$
3. $24\text{m}$
4. $6\text{m}$

Q. Motion of two objects are shown in the figure, which object has greater acceleration?

1. $A$
2. $B$
3. Both have equal acceleration
4. Can't say

Q. The acceleration of a particle starting from rest varies with time according to the relation $a=kt+c$. The velocity $v$ of the particle after time $t$ will be

1. $k{t}^2+ct$
2. $\frac{1}{2}(k{t}^2+ct)$
3. $\frac{1}{2}(k{t}^2+4ct)$
4. $\frac{k{t}^2}{2}+ct$

Q. On seeing a speed limit road sign, you apply brakes that bring your car from the speed of $30\text{m/s}$ to a speed of $20\text{m/s}$, covering a distance of $100\text{m}$ at a constant deceleration. How much time is required for the given decrease in speed?

1. $3\text{s}$
2. $4\text{s}$
3. $2\text{s}$
4. $5\text{s}$

Q. A parachutist drops first freely from an aeroplane for $10\text{s}$ and then parachute opens out. Now he descends with a net retardation of $2.5{\text{m/s}}^2$. If he bails out of the plane at a height of $2495\text{m}$ and $g=10{\text{m/s}}^2$, his velocity on reaching the ground in $\text{m/s}$ will be

Q. Choose the correct option:
i. Accelerated motion means acceleration and velocity have same direction.
ii. It is possible that particle have zero acceleration with non-zero velocity.
iii. When acceleration of the particle is positive, it is under accelerated motion.

1. Statement (i), (ii) and (iii) are true.
2. Statement (i) and (ii) are true.
3. Statement (ii) and (iii) are true.
4. Statement (i) and (iii) are true.

Q. If a particle moves with a constant velocity,

1. Its acceleration is positive
2. Its acceleration is negative
3. Its acceleration is zero
4. Its speed is zero

Q. A car starts from rest and accelerates at $5{\text{m/s}}^2$. At $t=4\text{s}$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6\text{s}$?

$(g=10{\text{m/s}}^2)$

1. $20\sqrt{2}\text{m/s},10{\text{m/s}}^2$
2. $20\text{m/s},5{\text{m/s}}^2$
3. $20\text{m/s},0{\text{m/s}}^2$
4. $20\sqrt{2}\text{m/s},0{\text{m/s}}^2$