Motion Under Variable Acceleration

Q.

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

1. Decreasing with time

2. Constant but not zero

3. Zero

4. Increasing with time

Q. The accleration of a particle is given by $a=(3t^2+2t+2)$ ${\text{ms}}^{-2}$ where $t$ is time. If the particle starts out with an initial velocity $v=2\text{m/s}$ at $t=0$, then the velocity of the particle at the end of $2\text{s}$ is

1. $12\text{m/s}$
2. $14\text{m/s}$
3. $16\text{m/s}$
4. $18\text{m/s}$

Q.

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is

1. 

2. 

3. 

4. 

Q. The position of a particle moving in the xy-plane at any time is given by $x=(3t^2-6t)$ metres, $y=(t^2-2t)$ metres. Select the correct statement about the moving particle from the following

1. The acceleration of the particle is zero at t = 0 second
2. The velocity of the particle is zero at t = 0 second
3. The velocity of the particle is zero at t = 1 second
4. The velocity and acceleration of the particle are never zero

Q. The initial velocity of a particle moving along x-axis is u(at t=0 and x=0) and its acceleration a is given by a=kx. Which of the following equation is correct between its ve locity(v) and (x)?

Q. The velocity of a body depends on time according to the equation $v=20+0.1t^2.$ The body is undergoing

1. Uniform acceleration
2. Uniform retardation
3. Non-uniform acceleration
4. Zero acceleration

Q.

The position x of a particle varies with time (t) as

x = 3t² – 2t³

The acceleration of the particle will be zero at time

1. 3 / 2

2. 1

3. 1 / 2

4. 0

Q.

A particle moving in a straight line has velocity and displacement equation as V = 4 $\sqrt{1+S}$ , where V in m/s and s is in m.

The initial velocity of the particle in m/s is ______

1. 7

2. 8

3. 9

4. 4

Q.

The v-s and $v^2$-s graph are given for two particles. Find the acceleration of the particles at s=0

1. 

2. 

3. 

4. 

Q.

The displacement x of a particle moving in one dimension is related to time t by the equation $t=\sqrt{x}+3$ where x is in metres and t in seconds. The displacement of the particle when its velocity is zero is

1. zero

2. 4 m

3. 1 m

4. 0.5 m

Q. A particle is moving with constant speed v along x axis in positive direction. Find the angular velocity of the particle about the point (0, b) when position of the particle is (a, 0)

Q.

The velocity of a particle moving along a straight line increases according to the linear law v = $v_0$ + kx

where k is a constant . Then

1) the accelearation of the particle is k($v_0$ + kx)

2) the particle takes a time $\frac{1}{k}$ $lo{g}_e$ ($\frac{v_1}{v_0}$) to attain a velocity $v_1$

3) velocity varies linearly with displacement with slope of velocity displacement curve equal to k

4) data is insufficient to arrive at a conclusion.

1. all of them are correct

2. 1 and 2 are correct

3. 2, 3 are correct

4. 1, 2, 3 are correct

Q.

When a particles displacement $\mathrm{x}$ at the time $\mathrm{t}$ is given by $\mathrm{x}={\mathrm{At}}^2+\mathrm{Bt}+\mathrm{C}$, where $\mathrm{A},\mathrm{B},\mathrm{and}\mathrm{C}$ are constants and $\mathrm{v}$ is the particles velocity, the number $4\mathrm{Ax}-{\mathrm{v}}^2$is found

1. $4\mathrm{AC}+{\mathrm{B}}^2$

2. $4\mathrm{AC}–{\mathrm{B}}^2$

3. $2\mathrm{AC}–{\mathrm{B}}^2$

4. $2\mathrm{AC}+{\mathrm{B}}^2$

Q.

The displacement of a particle is given by $\mathrm{x}={(\mathrm{t}-2)}^2$ where $\mathrm{x}$ is in meters and$\mathrm{t}$is in seconds. The distance covered by the particle in first $4$ seconds is?

Q.

A railroad car is moving I the +x direction on a straight and level track. A person in the railroad car throws a ball. The ball follows trajectory shown, relative to the railroad car. From an inspection of the trajectory, what can be concluded about the motion of railroad car? Treat y-axis along vertical.

1. it is moving at a constant speed

2. it is slowing down

3. it is speeding up

4. none of the above can be concluded

Q.

If velocity of a particle depends on time as v = $t^3+\frac{2}{\sqrt{t}}$. Then with what velocity is the particle moving at t = 4 sec and what is the displacement till then?

1. v = 64, d = 64

2. v = 65, d = 64

3. v = 65, d = 72

4. 

Q. Velocity-time equation of a particle moving in a straight line is, $v=(10+2t+3t^2)$. Find displacement of particle during $t=1\text{sec}$, if it is given that position is $20\text{m}$ at time $t=0\text{sec}.$

1. $12\text{m}$
2. $48\text{m}$
3. $32\text{m}$
4. $64\text{m}$

Q. A particle moving in a straight line has velocity and displacement equation as v=4\sqrt{1+s} where v is in m/s and s is in m the initial velocity of the particle is

Q.

A particle retards from a velocity $v_0$ while moving in a straight line. If the magnitude of deceleration is directly proportional to the square root of the speed of the particle, find its average velocity for the total time of its motion.

1. 

2. 

3. 

4. 

Q. particle moving with uniform acceleration alongX-axis crosses the points x = 2 m and x = 7 m withvelocities 5 ms-1 and 15 ms-1 respectively. Thevelocity with which it crosses point x = 3 m is(1) 65 ms(2) 10 ms-1(3)50 ms(4) 35 ms1

Q. Figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at $t=0.3s,1.2s,-1.2s.$

Q. The position of a particle moving along x axis is given by x=At+4Bt3 what is its velocity at t=5s?

Q. 110.Find relation between velocity (v) and position (x) if particle moving along x axis with acceleration a=Kx initially partial moving with speed u at t=0 and x=0

Q. A charged particle having drift velocity of $7.5\times {10}^{-4}{\text{ms}}^{-1}$ in an electric field of $3\times {10}^{-10}{\text{Vm}}^{-1}$, has a mobility of (in${\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$)

Q.

A particle located at x = 0, at time t = 0 starts moving along the positive x direction with a velocity v that varies as v = $\alpha$ $\sqrt{x}$.The displacement of the particle varies with time as

1. $t^3$

2. $t^2$

3. t

4. $t^{\frac{1}{2}}$

Q.

An ant starts from the origin and walks along a straight line. After every second, its position (in mm) is observed by a curious 5-year old. These are his readings:

Position (mm) 0 10 40 100 200

After time (s) 0 1 2 3 4

By looking at this table, which of the following could be a possible description of the ant's motion is

(a) Uniform velocity (b) uniform acceleration (with non-uniform velocity

(c) Uniform jerk (with non-uniform accelerator) (d) cannot be determined (can be any of the above)

1. Uniform jerk (with non-uniform accelerator)

2. uniform acceleration (with non-uniform velocity

3. cannot be determined (can be any of the above)

4. Uniform velocity

Q. 47.The position of a body moving along x axis given by x= (2t3 + 3t2 + 5). The acceleration of particle at the instant its velocity becomes zero is

Q.

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4t^3-2t)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin

1. $28m/s^2$

2. $22m/s^2$

3. $12m/s^2$

4. $10m/s^2$

Q. { †ext { The } x †ext { and } y †ext { coordinates of a particle at any time } t †ext { are given } } { †ext { by } x = 7 t + 4 t ^ { 2 } †ext { and } y = 5 t †ext { , where } x †ext { and } y †ext { are in metre and } } { t †ext { in seconds. The acceleration of particle at } t = 5 s †ext { is }

Q.

Two particles move along x axis. the position of particle 1 is given by x = 6.00$t^2$ + 3.00t + 2.00 (in meters and seconds); the acceleration of particle 2 is given by a = -8.00t ( in meters per second squared and seconds) and, at t = 0, its velocity is 19 m/s. When the velocities of the particles match, what is their velocity?

1. 1

2. 2

3. 3

4. 4