Different Kinds of Motion

Q. If a body starts from rest and travels $120\text{cm}$ in the $6^{th}$ second, then the acceleration of the body is

1. $0.2m/s^2$
2. $0.027m/s^2$
3. $0.218m/s^2$
4. $0.03m/s^2$

Q. A body starts from rest. What is the ratio of the distance travelled by the body during the $4^{th}$ and $3^{rd}$ second ?

1. $\frac{7}{5}$
2. $\frac{5}{7}$
3. $\frac{7}{3}$
4. $\frac{3}{7}$

Q. A body of mass $2\text{kg}$ moving with a speed of $4\text{m/s}$ makes an elastic collision with another body at rest. It continues to move in the original direction but with one fourth of its initial speed. The speed of the center of mass of the two bodies is $\frac{x}{10}\text{m/s}$. Then the value of $x$ is

Q. A body starts from rest and travels $s\text{m}$ in $2^{nd}$ second, then, acceleration is

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

Q. The initial velocity of the particle is $10\text{m/sec}$ and its retardation is $2{\text{m/sec}}^2$. The distance moved by the particle in $5^{\text{th}}$ second of its motion is

1. $1\text{m}$
2. $19\text{m}$
3. $50\text{m}$
4. $75\text{m}$

Q. A truck starts from rest with an acceleration of $1.5{\text{m/s}}^2$ while a car $150\text{m}$ behind starts from rest with an acceleration of $2{\text{m/s}}^2$. What is the distance travelled by the car before it gets side by side to the truck?

1. $300\text{m}$
2. $400\text{m}$
3. $600\text{m}$
4. $800\text{m}$

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 $x=4m$, then which of the following are correct? (Given velocity is in $m/s$ and position is in $m$)

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

Q. Two cars $A$ and $B$ are at rest and at the same point initially. If $A$ starts with uniform velocity of $40\text{m/s}$ and $B$ starts in the same direction with constant acceleration of $4{\text{m/s}}^2$ , then $B$ will catch $A$ after the time

1. $10\text{s}$
2. $20\text{s}$
3. $35\text{s}$
4. $30\text{s}$

Q. A particle is moving in a straight line such that its velocity is increasing at $5{\text{ms}}^{-1}$ per meter. The acceleration of the particle is ${\text{ms}}^{-2}$ at a point where its velocity is $20{\text{ms}}^{-1}$.

Q. A body, moving in a straight line with an initial velocity of $5{\text{ms}}^{-1}$ and a constant acceleration, covers a distance of $30\text{m}$ in the $3^{rd}$ second. How much distance will it cover in the next $2$ seconds?

1. $90\text{m}$
2. $100\text{m}$
3. $70\text{m}$
4. $80\text{m}$

Q.

The velocity displacement graph of a particle moving along a straight line is shown

The most suitable acceleration -displacement $(a-x)$ graph will be

1. 

2. 

3. 

4. 

Q. A body starts from rest and travels $s\text{m}$ in $2^{nd}$ second, then, acceleration is

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

Q. A body starting from rest moving with uniform acceleration has a displacement of $16\text{m}$ in first $4\text{s}$ and $9\text{m}$ in first $3\text{s}$. the acceleration of the body is

1. $1{\text{ms}}^{-2}$
2. $2{\text{ms}}^{-2}$
3. $3{\text{ms}}^{-2}$
4. $4{\text{ms}}^{-2}$

Q.

A particle covers equal distance in equal interval of time, It is said to be moving with uniform

1. Speed

2. Acceleration

3. Velocity

4. Retardation

Q. A particle having initial velocity $10\text{m/s}$ is moving with constant acceleration $4{\text{m/s}}^2$. The particle is moving in a straight line. Find the distance travelled by the particle in $7^{th}$ second of its motion

1. $10\text{m}$
2. $36\text{m}$
3. $5\text{m}$
4. $28\text{m}$

Q.

A particle executes S.H.M., the graph of velocity as a function of displacement is:

1. a circle

2. a parabola

3. an ellipse

4. a helix

Q. Consider a particle initially moving with a velocity of $5\text{m/s}$ starts decelerating at a constant rate of $2m/s^2$. Find the distance travelled in the $2^{nd}$ second.

1. $2\text{m}$
2. $1\text{m}$
3. $5\text{m}$
4. $8\text{m}$

Q. If body having initial velocity zero is moving with uniform acceleration of $8{\text{m/sec}}^2$, the distance travelled by it in fifth second will be

1. $36\text{m}$
2. $40\text{m}$
3. $30\text{m}$
4. $\text{Zero}$

Q. The initial velocity of a body moving along a straight line is $7\text{m/s}$. It has a uniform acceleration of $4{\text{m/s}}^2$. The distance covered by the body in the $5^{\text{th}}$ second of its motion is

1. $35\text{m}$
2. $25\text{m}$
3. $30\text{m}$
4. $15\text{m}$

Q.

The displacement of the particle (in $m$) is given by

$y=2t+t^2-2t^3$

What is the velocity (in $m/s$) of the particle at the instant when its acceleration is zero?

1. $\frac{5}{2}$
2. $\frac{2}{5}$
3. $\frac{13}{6}$
4. $\frac{6}{13}$

Q. The graph (Fig) below describes the motion of a ball rebounding from a horizontal surface being released from a point above the surface. Assume the ball collides each time with the floor inelastically. The quantity represented on the y-axis is the ball's (take upward direction as positive)

1. Displacement
2. Velocity
3. Acceleration
4. Momentum

Q. Figure (i) and (ii) below show the displacement time graphs of two particles moving along the $x–$axis. We can say that

1. Particle (i) is speeding up while particle (ii) is speeding down.
2. Both the particles are speeding up.
3. Both the particles are speeding down.
4. Particle (i) is speeding down while particle (ii) is speeding up.

Q. Starting from rest a particle is first accelerated for time $t_1$ with constant acceleration $a_1$ and then stops in time $t_2$ with constant retardation $a_2.$ Let $v_1$ be the average velocity in this case and $s_1$ the total displacement.
In the second case, it is accelerated for the same time $t_1$ with constant acceleration $2a_1$ and comes to rest with constant retardation $a_2$ in time $t_3.$ If $v_2$ is the average velocity in this case and $s_2$ the total displacement, then:

1. $v_2=2v_1$
2. $2v_1<v_2<4v_1$
3. $s_2=2s_1$
4. $2s_1<s_2<4s_1$

Q. The motion of a particle along a stright line is described by the equation $x=8+12t-t^3$ where, $x$ is in meter and $t$ in second. The retardation of the particle when its velocity beocmes zero, is

1. $12{\text{ms}}^{-2}$
2. $\text{Zero}$
3. $6{\text{ms}}^{-2}$
4. $24{\text{ms}}^{-2}$

Q. A body started with a velocity of $20m{s}^{-1}$ and moving with an acceleration of $2m{s}^{-2}$. The distance (in $\text{m})$ travelled by the body in the $8^{th}$ second is

1. $12$
2. $10$
3. $20$
4. $35$

Q. The initial velocity of a particle is $10\text{m/sec}$ and its retardation is $2{\text{m/sec}}^2$. The distance covered in the fifth second of the motion will be

1. $1\text{m}$
2. $9\text{m}$
3. $5\text{m}$
4. $7\text{m}$

Q. For a particle moving along $+x$-axis, which of the following velocity-position graphs is possible (position is represented by $x$ - coordinate of the particle)

1. 
2. 
3. 
4. None of these

Q. As a car passes the point $A$ on a straight road, its speed is $10\text{m/s}$. The car moves with constant acceleration $a{\text{m/s}}^2$ along the road for $T$ seconds until it reaches the point $B$, where its speed is $v\text{m/s}$. The car travels at this speed for a further $10$ seconds, when it reaches the point $C$. From $C$ it travels for a further $T$ seconds with constant acceleration $3a{\text{m/s}}^2$ until it reaches a speed of $20\text{m/s}$ at the point $D$. Choose the correct option(s).
[Given that the distance between $A$ and $D$ is $675\text{m}$]

1. value of $v$ is $12.5\text{m/s}$
2. value of $a$ is $\frac{1}{8}{\text{m/s}}^2$
3. value of $T$ is $10\text{s}$
4. value of $T$ is $20\text{s}$

Q. A body starts from rest. What will be the ratio of the distance travelled by the body during the $4^{th}$ and $3^{rd}$ second?

1. $7/5$
2. $7/3$
3. $5/7$
4. $3/7$

Q. A ball is dropped vertically from a height $10\text{m}$ above the ground. It hits the ground and bounces up vertically to a height of $5\text{m}$. Neglecting subsequent motion and air resistance, which of the following options correctly represents the variation of its velocity $v$ with height $h$ above the ground.

1. 
2. 
3. 
4.