Uniform and Non Uniform

Q.

A bullet is fired on a wall with velocity 100ms^-1. If the bullet stops at a depth of 10cm inside the wall, find the retardation produced by the wall.

Q.

When a particles distance traveled is proportional to the squares of time, the particle travels with

1. Uniform acceleration

2. Uniform velocity

3. Increasing acceleration

4. Decreasing velocity

Q.

The distance traveled by car in $\mathrm{t}$ seconds after applying the brakes is $\mathrm{s}$ feet, where $\mathrm{s}=22\mathrm{t}–12{\mathrm{t}}^2$. The car travels a certain distance before coming to a complete halt.

1. $10.08ft$

2. $10ft$

3. $11ft$

4. $11.5ft$

Q.

The equation of motion of a car is $s=t^2–2t$, where is measured in hours and s in kilometres. When the distance travelled by a car is $15km$, the velocity of the car is

1. $2km/hr$

2. $4km/hr$

3. $3km/hr$

4. $8km/hr$

Q.

The following relation [in MKS units] gives the distance traversed s by an accelerated particle of mass $\mathrm{M}:\mathrm{s}=6\mathrm{t}+3{\mathrm{t}}^2$. The particles velocity after $2$ seconds in the appropriate unit is

1. $6$

2. $12$

3. $18$

4. $24$

Q.

$\mathrm{s}=3–4\mathrm{t}+5{\mathrm{t}}^2$ is the distance traveled by an item along a straight line in time $\mathrm{t}$, and the beginning velocity of the object is

1. $3units$

2. $–3units$

3. $4units$

4. $–4units$

Q. A balloon rises from ground with an initial velocity of zero, and its acceleration decreases with height linearly. Its acceleration at ground is $a_0$ and decreases to zero at height $H_0$ then

1. Maximum velocity of balloon will be $\sqrt{a_0{H}_0}$
2. Maximum velocity of balloon will be $2\sqrt{a_0{H}_0}$
3. Velocity when it is at height $\frac{H_0}{2}$ is $\frac{\sqrt{3a_0{H}_0}}{2}$
4. Velocity when it is at height $\frac{H_0}{2}$ is $\sqrt{a_0{H}_0}$

Q. The relation$3t=\sqrt{3x}+6$describes the displacement of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is

1. $24metres$
2. $12metres$
3. $5metres$
4. $Zero$

Q.

The equation of motion of a car is , $s=t^2-2t$ where t is measured in hours and s is measured in kilometers. If the distance traveled by car is 15 km, find the velocity of the car

1. $4\frac{km}{h}$

2. $2\frac{km}{h}$

3. $3\frac{km}{h}$

4. $8\frac{km}{h}$

Q. The position of particle travelling along x-axis is given by $x_t=t^3–9t^2+6t$ where $x_t$ is in $\text{cm}$ and $t$ is in second. Then–

1. The body comes to rest first at $(3–\sqrt{7})s$ and then at $(3+\sqrt{7})s$
2. The total displacement of the particle in travelling from the first zero of velocity to the second zero of velocity is zero
3. The total displacement of the particle in travelling from the first zero of the velocity to the second zero of velocity is $–74cm$
4. The particle reverses it’s velocity at $(3–\sqrt{7})s$ and then at $(3+\sqrt{7})s$ and has a negative velocity for $(3–\sqrt{7})s<t<(3+\sqrt{7})s$

Q. A particle is moving along the $x$-axis. Its velocity $\left(v\right)$ with $x$ co-ordinate is varying as $v=\sqrt{x}$. Then

1. Initial velocity of particle is zero
2. Motion is non-uniformly accelerated
3. Acceleration of particle at $x=2m\text{is}\frac{1}{2}m/s^2$
4. Acceleration of particle at $x=4m\text{is}1m/s^2$

Q. The speed $v$ of a car moving on a straight road changes according to equation, $v^2=a+bx$, where $a$ and $b$ are positive constants. Then, the magnitude of acceleration in the course of such motion: ($x$ is the distance travelled) :

1. Increases
2. Decreases
3. Stays constant
4. First decreases and then increases

Q. A particle moves along x-axis and its acceleration at any time $t$ is $a=2sin\left(\pi t\right)$, where $t$ is in seconds and $a$ is in $m/s^2$. The initial velocity of particle (at time $t=0$) is $u=0$.
Then the magnitude of displacement (in meters) by the particle from time $t=0$ to $t=t$ will be

1. $\frac{2}{{\pi }^2}\sin \pi t-\frac{2t}{\pi }$
2. $-\frac{2}{{\pi }^2}\sin \pi t+\frac{2t}{\pi }$
3. $\frac{2t}{\pi }$
4. None of these

Q. A car accelerates from rest with a constant acceleration $\alpha$ on a straight road. After gaining a velocity $v$, the car moves with the same velocity for some time. Then the car is decelerated to rest with a retardation $\beta$. If the total distance covered by the car is equal to $S$, the total time taken for its motion is

1. $\frac{S}{v}+\frac{v}{2}(\frac{1}{\alpha }+\frac{1}{\beta })$
2. $\frac{S}{v}+\frac{v}{\alpha }+\frac{v}{\beta }$
3. $(\frac{v}{\alpha }+\frac{v}{\beta })$
4. $\frac{S}{v}-\frac{v}{2}(\frac{v}{\alpha }+\frac{v}{\beta })$

Q. When acceleration be function of velocity as $a=f\left(v\right)$, then

1. The displacement $\left(x\right)=\int \frac{vdv}{f\left(v\right)}$
2. The acceleration may be constant
3. The slope of acceleration versus velocity graph may be constant.
4. (a) and (c) are correct.

Q.

The velocity of a particle varies with time at $v\left(t\right)=e^{-2\pi t}$. Find the displacement of the particle till $t=(\frac{1}{2\pi })$ sec.

1. $-\frac{\left(1\right)}{2\pi e}$

2. $\frac{1}{2\pi e}$e

3. $\frac{(e-1)}{2\pi e}$

4. $\frac{1}{e}$

Q. The $x$ coordinate 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. A particle is moving along x-axis whose instantaneous speed is $v=\sqrt{108-9x^2}$. The acceleration of the particle is

1. $-9x{\text{m/s}}^2$
2. $-18x{\text{m/s}}^2$
3. $\frac{-9x}{2}{\text{m/s}}^2$
4. None of these

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 balloon rises from ground with an initial velocity of zero, and its acceleration decreases with height linearly. Its acceleration at ground is $a_0$ and decreases to zero at height $H_0$ then

1. Maximum velocity of balloon will be $\sqrt{a_0{H}_0}$
2. Maximum velocity of balloon will be $2\sqrt{a_0{H}_0}$
3. Velocity when it is at height $\frac{H_0}{2}$ is $\frac{\sqrt{3a_0{H}_0}}{2}$
4. Velocity when it is at height $\frac{H_0}{2}$ is $\sqrt{a_0{H}_0}$

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. The displacement travelled by a particle in a straight-line motion is directly proportional to $t^{1/2}$, where $t=$ time elapsed. What is the nature of motion?

1. Increasing acceleration
2. Decreasing acceleration
3. Increasing retardation
4. Decreasing retardation

Q. A particle is moving in a straight path with an acceleration $a=bn$, where $b$ is a positive constant $(n\ne -1)$. Assuming particle is at rest at origin at $t=0$, the relation between the velocity and the position$\left(r\right)$ of the particle at time $t=1\text{s}$ is

(Assume SI units)

1. $v=r$
2. $v=2r$
3. $v=\frac{(n+3)r}{2}$
4. $v=\frac{(n+1)r}{2}$

Q. A particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown, which of the following statements is/are correct ?

1. Curve 1 may represent acceleration against time graph
2. Curve 2 may represent velocity against time graph
3. Curve 2 may represent velocity against acceleration graph
4. None of these

Q. The velocity of a particle moving in the positive direction of $x-$ axis varies as $v=10\sqrt{x}$ ($v$ is in ${\text{ms}}^{-1},x$ is in $m$). Assuming that at $t=0,$ particle was at $x=0$. Then,

1. The initial velocity of the particle is zero
2. The initial velocity of the particle is $2.5{\text{ms}}^{-1}$
3. The acceleration of the particle is $2.5{\text{ms}}^{-2}$
4. The acceleration of the particle is $50{\text{ms}}^{-2}$

Q. A point moves in a straight line so that its displacement $x$ at time $t$ is given by equation $x^2=t^2+1$. Its acceleration is:

1. $\frac{1}{x}$
2. $\frac{1}{x^3}$
3. $-\frac{1}{x^2}$
4. $-\frac{1}{x^3}$

Q. The velocity of a particle moving in the positive direction of $x-$ axis varies as $v=10\sqrt{x}$ ($v$ is in ${\text{ms}}^{-1},x$ is in $m$). Assuming that at $t=0,$ particle was at $x=0$. Then,

1. The initial velocity of the particle is zero
2. The initial velocity of the particle is $2.5{\text{ms}}^{-1}$
3. The acceleration of the particle is $2.5{\text{ms}}^{-2}$
4. The acceleration of the particle is $50{\text{ms}}^{-2}$

Q. A particle moves along x-axis and its acceleration at any time $t$ is $a=2sin\left(\pi t\right)$, where $t$ is in seconds and $a$ is in $m/s^2$. The initial velocity of particle (at time $t=0$) is $u=0$.
Then the distance travelled (in meters) by the particle from time $t=0$ to $t=t$ will be

1. $\frac{2}{{\pi }^2}\sin \pi t-\frac{2t}{\pi }$
2. $-\frac{2}{{\pi }^2}\sin \pi t+\frac{2t}{\pi }$
3. $\frac{2t}{\pi }$
4. None of these

Q. The speed $v$ of a car moving on a straight road changes according to equation, $v^2=a+bx$, where $a$ and $b$ are positive constants. Then, the magnitude of acceleration in the course of such motion: ($x$ is the distance travelled) :

1. Increases
2. Decreases
3. Stays constant
4. First decreases and then increases

Q. A particle is moving rectilinearly so that its acceleration is given as $a\left(m/s^2\right)=3t^2+1$ Its initial velocity is zero then the velocity of the particle at $t=1$ s will be

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