Introduction to acceleration

Q.

A body is moving with a velocity of $10m/s$. If the motion is uniform, what will be the velocity after 10 seconds?

Q.

Can an object be accelerated without speeding up or slowing down?

Q. The acceleration will be positive in which of the following graphs?

1. (I) and (III)
2. (I) and (IV)
3. (II) and (IV)
4. None of these

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. 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. The average velocity of a body moving with uniform acceleration travelling a distance $3.06\text{m}$ is $0.34\text{m/s}$. If the change in velocity of the body is $0.18\text{m/s}$ during this time, its uniform acceleration is

1. $0.01{\text{m/s}}^2$
2. $0.02{\text{m/s}}^2$
3. $0.03{\text{m/s}}^2$
4. $0.04{\text{m/s}}^2$

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. Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is:

1. Increases linearly with $x$
2. Constant
3. Increases parabolically with $x$
4. None

Q. A car accelerates uniformly from $13\text{m/s}$ to $31\text{m/s}$ while entering the motorway, covering a distance of $220\text{m}$. Then the acceleration of the car will be:

1. $2.9{\text{m/s}}^2$
2. $1.8{\text{m/s}}^2$
3. $4{\text{m/s}}^2$
4. $2.2{\text{m/s}}^2$

Q. The displacement of a body in $8\text{s}$, starting from rest, with an acceleration of $20{\text{cm/s}}^2$ is

1. $64\text{m}$
2. $64\text{cm}$
3. $640\text{cm}$
4. $0.064\text{m}$

Q. A particle is moving along $x$-axis whose acceleration is given as $a=3x–4$, where $x$ is the location of the particle. At $t=0$, the particle is at rest at $x=4/3$. The distance travelled by the particle in 5 seconds is

1. Infinite
2. $\approx 42\text{m}$
3. Zero
4. None of these

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. For uniformly accelerated motion, both magnitude and of acceleration must remain constant.

1. strength
2. direction
3. speed

Q. The displacement $\left(x\right)$ of a particle along a straight line at time $t$ is given by $x=a_0+\frac{a_1}{2}t+\frac{a_2}{3}{t}^2$, the acceleration of the particle is

1. $a_1/2$
2. $a_2/3$
3. $a_0+a_2/3$
4. $2a_2/3$

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.

	Column I		Column II
(A)	$\overrightarrow{a}\perp \overrightarrow{v},a\ne 0$	(P)	Speed is constant
(B)	$\overrightarrow{a}\parallel \overrightarrow{v},a\ne 0$	(Q)	Velocity is constant
(C)	$\overrightarrow{a}=0$	(R)	Speed is variable
(D)	$a\ne 0,\overrightarrow{a}$ neither parallel to $\overrightarrow{v}$ nor $\perp \overrightarrow{v}$	(S)	Motion is along a line

Which of the following options has the correct combination considering column-I and column-II ?

1. B → R, S
2. A → Q
3. D → S
4. C → P, Q

Q. The position of the particle is given by $x\left(t\right)=(4t^2-3t+2t^3)$, its acceleration will be

1. $4t+2t^2$
2. $12t^2+8t$
3. $8t-3+6t^2$
4. $12t+8$

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 adjoining figures gives the velocity-time graph. This shows that the body is

1. Starting from rest and moving with uniform velocity
2. Moving with uniform retardation
3. Moving with varying acceleration
4. Having same initial and final velocity

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 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. Assertion: A body can have an acceleration even if its velocity is zero at a given instant of time.
Reason: A body is momentarily at rest when it reverses its direction of motion.

1. If both assertion and reason are true and the reason is correct explanation of the assertion
2. If both assertion and reason are true, but reason is not correct explanation of the assertion
3. The assertion is true, but the reason is false
4. The assertion is false and reason is true

Q. Assertion : A positive acceleration of a body can be associated with a ‘slowing down’ of the body.
Reason : Acceleration is a vector quantity.

1. If both assertion and reason are true and the reason is the correct explanation of the assertion.
2. If both assertion and reason are true but reason is not the correct explanation of the assertion.
3. If assertion is true but reason is false.
4. If the assertion and reason both are false.
5. If assertion is false but reason is true.

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. Assertion : A positive acceleration of a body can be associated with a ‘slowing down’ of the body.
Reason : Acceleration is a vector quantity.

1. If both assertion and reason are true and the reason is the correct explanation of the assertion.
2. If both assertion and reason are true but reason is not the correct explanation of the assertion.
3. If assertion is true but reason is false.
4. If the assertion and reason both are false.
5. If assertion is false but reason is true.

Q. The position $x$ of a body as a function of time $t$ is given by the equation:
$x=2t^3-6t^2+12t+16$
The acceleration of the body is zero at time $t$ is equal to

1. $1\text{s}$
2. $2\text{s}$
3. $3\text{s}$
4. $0.5\text{s}$

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 relation between time and distance 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. $2{\beta }^2{v}^3$

Q. A ball crosses point p with speed 6 $m/s$ and returns same point p with speed 8 $m/s$ in 5 seconds. Assuming acceleration($a$) is uniform, find the magnitude of $a$

1. $\frac{8}{5}m/s^2$
2. $\frac{6}{5}m/s^2$
3. $\frac{5}{5}m/s^2$
4. $\frac{14}{5}m/s^2$