2nd Equation of Motion

Q.

A bus starting from rest moves with a uniform acceleration of $0.1m/s^2$ for $2mins$. Find

1. the speed acquired,
2. the distance traveled.

Q.

A trolley, while going down an inclined plane, has an acceleration of $2cm{s}^{-2}$. What will be its velocity $3s$ after the start?

Q. Calculate the total electric flux linked with a circular disc of radius a is situated at distance R from a point charge q

Q.

Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of $72km{h}^{-1}$ in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by $1m/s^2$. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

Q.

Show that path of projectile is parabola?

Q.

A particle travels $\text{10m}$ in first $\text{5sec}$ and $\text{10m}$ in next $\text{3sec}$ . Assuming constant acceleration what is the distance travelled in next $\text{2sec.}$

1. 10.3 m
2. 9.3 m
3. None of above
4. 8.3 m

Q.

A particle experiences constant acceleration for $20$ seconds after starting from rest. If it travels a distance $s_1$ in the first $10$ seconds and distance $s_2$ in the next $10$ seconds, then

1. $s_2=s_1$
2. $s_2=2s_1$
3. $s_2=3s_1$
4. $s_2=4s_1$

Q. A car starts moving along a line, first with acceleration $a=5\frac{m}{s^2}$ starting from rest, then uniformly, and finally decelerating at the same rate $a$ to come to rest. The total time of motion is $25s$. The average speed during the time is $20\frac{m}{s}.$ How long does the particle move uniformly?

Q. A quarter ring of radius is having uniform charge density.Find the electric field and potential at the centre of ring.

Q.

A particle moving with a uniform acceleration travels $24m$ and $64m$ in the first two consecutive intervals of $4s$ each. Its initial velocity will be.

1. $5\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

2. $3\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

3. $4\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

4. $1\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Q. A particle starts from rest, accelerates at$2m/s^2$for 10s and then goes for constant speed for 30s and then decelerates at$2m/s^2$ till it stops. What is the distance travelled by it

1. 800 m
2. 750 m
3. 700 m
4. 850 m

Q. A ball is released from the top of a tower of height h metres. It takes T seconds to reach the ground. What is the position of the ball at T/3 second?

Q. A car starts from rest and moves with uniform acceleration a on a straight road from time t = 0 to t = T. After that, a constant deceleration brings it to rest. In this process the average speed of the car is

1. 
2. 
3. 
4. 

Q.

In the third second, the distance traveled by a particle starting from rest and traveling with an acceleration of $4/3{\mathrm{ms}}^{-2}$ is

1. $\left(\frac{10}{3}\right)m$

2. $\left(\frac{19}{3}\right)m$

3. $6m$

4. $4m$

Q. The velocity of a bullet is reduced from $200\text{m/s}$ to $100\text{m/s}$ while travelling through a wooden block of thickness $10\text{cm}$. The retardation, assuming it to be uniform, will be

1. $10\times {10}^4{\text{m/s}}^2$
2. $12\times {10}^4{\text{m/s}}^2$
3. $13.5\times {10}^4{\text{m/s}}^2$
4. $15\times {10}^4{\text{m/s}}^2$

Q.

The motion of a particle along a straight line is described by equation x=8+12t -t^{3 ,} ​​^​, where x is in metre and t is in second. What is the retardation of the particle when its velocity becomes zero

Q. prove that time of ascent = time of decent

Q.

A ball is thrown vertically upwards attains a maximum height of 45m. What is the time after which velocity of the ball become equal to half the velocity of projection?

Q. A particle starts with an initial velocity $2.5\text{m/s}$ along the positive $x-$ direction and it accelerates uniformly at the rate $0.50{\text{m/s}}^2$. The distance travelled by the particle in first two seconds will be

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

Q. A car starts from rest and moves with uniform acceleration$a$ on a straight road from time$t=0tot=T$. After that, a constant deceleration brings it to rest. In this process the average speed of the car is

1. 
2. 
3. 
4. 

Q. A body starts from rest and is uniformly accelerated for $30\text{s}$. The distance travelled in the first $10\text{s}$ is $x_1$, next $10\text{s}$ is $x_2$ and the last $10\text{s}$ is $x_3$. Then $x_1:x_2:x_3$ is the same as

1. $1:2:4$
2. $1:2:5$
3. $1:3:5$
4. $1:3:9$

Q.

Let $m_1=1$kg $m_2=2$kg and $m_3=3$ kg in figure.

Find the accelerations of $m_1,m_2,$ and $m_3$. The string from the upper pulley to $m_1$ is 20 cm when the system is released from rest. How long will it take before $m_1$ strikes the pulley ?

Q. The engine of a motorcycle can produce a maximum acceleration$5m/s^2$ . Its brakes can produce a maximum retardation$10m/s^2$. What is the minimum time in which it can cover a distance of 1.5 km

1. 30 sec
2. 15 sec
3. 10 sec
4. 5 sec

Q. A body covers $200cm$ in the first $2$ seconds and $220cm$ in the next $4$ seconds. The velocity of the body at the end of the $7^{th}$ second is

1. $10cm/s$
2. $20cm/s$
3. $5cm/s$
4. $30cm/s$

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

Q. A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be

1. 2.5 m/s
2. 5.5 m/s
3. 11 m/s
4. 4 m/s

Q. A particle is projected from horizontal making an angle ${60}^{\circ }$ with initial velocity 40 m/s. Find the time taken to the particle to make angle ${45}^{\circ }$ from horizontal.

1. $2.5s$
2. $3.5s$
3. $1.5s$
4. $4.5s$

Q. A particle of mass $m$ and charge $-q$ is projected from the origin with a horizontal speed $v$ into a space having electric field of magnitude $E$ directed downwards as shown in the figure. If the effect due to gravity can be neglected, then choose the correct statement(s) among the following.

1. The kinetic energy after a displacement $y$ is $qEy$
2. The horizontal and vertical components of acceleration are $a_x=0,a_y=\frac{qE}{m}$
3. The equation of trajectory is $y=\frac{1}{2}\left(\frac{q{E}_x^2}{m{v}^2}\right)$
4. The horizontal and vertical displacements $x$ and $y$ after a time $t$ are $x=vt$ and $y=\frac{1}{2}{a}_y{t}^2$

Q. A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is

1. 9/25
2. 3/5
3. 25/9
4. 1/25

Q. Two cars A and B are moving towards each other on a straight road with velocity 10 m/sec. and 12 m/sec. respectively. When they are 160 m apart, each car decelerates at $2{\text{m/sec}}^2$ until they stop in order to avoid collision. Calculate the distance (in $m$) between them when they come to rest.