3rd Equation of Motion

Q. A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

1. 
2. 
3. 
4. 

Q. 70. A hunter has a machine gun that can fire 50g bullet with a velocity of 150 m/s. A 60 kg tiger spring at him with the velocity of 10 m/s. How many bullet must the hunter fire per second into tiger in order to stop him in his track

Q.

A bullet on penetrating $30cm$ into its target loses its velocity by $50\%$. What additional distance will it penetrate into the target before it comes to rest?

1. $30cm$

2. $20cm$

3. $10cm$

4. $5cm$

Q.

The velocity of kerosene oil in a horizontal pipe is 5 m/s. If then the velocity head of oil will be

1. 1.25 m

2. 12.5 m

3. 125 m

4. 0.125 m

Q. if v =x^2-5x+4 , find the acceration of the particle when velocity of the particle is

Q. A car moving along a straight highway with speed of 126 km h¯¹ is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop ?

Q. what is sum error?how to derive z(sum of error) from a and b?

Q. 1. Derive the expressions for elastic collision in one dimension and also discuss their two special cases?2. Derive the equations of a uniformly accelerated motion by calculus method.

Q. A body travels for $15sec$ starting from rest with constant acceleration. If it travels distances $s_1,s_2$ and $s_3$ in the first five seconds, second five seconds and next five seconds respectively, the relation between $s_1,s_2$ and $s_3$ is

1. $s_1=\frac{1}{3}{s}_2=\frac{1}{5}{s}_3$
2. $s_1=\frac{1}{5}{s}_2=\frac{1}{3}{s}_3$
3. $2s_1=\frac{1}{3}{s}_2=\frac{1}{5}{s}_3$
4. $s_1=\frac{1}{6}{s}_2=\frac{1}{5}{s}_3$

Q. Two car travelling towards each other on a straight road at velocity $10\text{m/sec}$ and $12\text{m/sec}$ respectively. When they are $150\text{m}$ apart, both drivers apply their brakes and each car decelerates at $2\text{m}/{\text{sec}}^2$ until it stops. How far apart will they be when they have both come to a stop ?

Q. A body having its centre of mass at the origin has three of its particles at (a, 0, 0), (0, a, 0), (0, 0, a). The moments of inertia of the body about the X and Y axes are 0⋅20 kg-m² each. The moment of inertia about the Z-axis
(a) is 0⋅20 kg-m²
(b) is 0⋅40 kg-m²
(c) is $0·20\sqrt{2}$ kg-m²
(d) cannot be deduced with this information.

Q. A body moving in a straight line with constant acceleration of $10{\text{ms}}^{-2}$ covers a distance of $40\text{m}$ in the $4^{th}$ second. How much distance will it cover in the $6^{th}$ second?

1. $50\text{m}$
2. $60\text{m}$
3. $70\text{m}$
4. $80\text{m}$

Q. A driver, having a definite reaction time, is capable of stopping over a distance of $30\text{m}$ on seeing a red traffic light when speed of the car is $72\text{km/hr}$ and over a distance of $10\text{m}$ when the speed is $36\text{km/hr}$. Assuming that his reaction time and the acceleration of the car remain the same in all cases, find the distance over which he can stop the car when he is going at $54\text{km/hr}$.

1. $11.75\text{m}$
2. $13.75\text{m}$
3. $15.75\text{m}$
4. $18.75\text{m}$

Q.

A bullet moving with a velocity of 200 cm/s penetrates a wooden block and comes to rest after traversing 4 cm inside it. What velocity is needed for travelling distance of 9 cm in same block?

1. 100 cm/s

2. 136.2 cm/s

3. 300 cm/s

4. 250 cm/s

Q. A balloon starts from rest is rising upwards with constant acceleration $15{\text{m/s}}^2$ and after $10\text{s}$, a packet is dropped from it. The packet reaches the ground after $t_0\text{sec}$. Determine the value of $t_0$ (in sec). Take $g=10{\text{m/s}}^2$ and $\sqrt{15}=3.87$.

1. $21.4$
2. $34.33$
3. $25.5$
4. $30.7$

Q. A bullet fired into a fixed target loses half of its velocity after penetrating$3cm$. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

1. 1.5 cm
2. 1.0 cm
3. 3.0 cm
4. 2.0 cm

Q. A car is moving from A to B in straight line at constant acceleration. If velocities at A and B are u and v respectively, then velocity at the midpoint of A and B is

1. $\frac{v+u}{2}$
2. $\frac{2uv}{4+v}$
3. $\sqrt{\frac{u^2+v^2}{2}}$
4. $\frac{v-u}{2}$

Q. A particle starts from rest and has an acceleration of $2{\text{m/s}}^2$ for 10 sec. After that, it travels for 30 sec with constant speed and then undergoes a retardation of $4{\text{m/s}}^2$ and comes back to rest. The total distance covered by the particle is

1. $650\text{m}$
2. $750\text{m}$
3. $700\text{m}$
4. $800\text{m}$

Q. A Carnot engine operates with an efficiency equals to $\frac{1}{5}$. On decreasing the temperature of the sink by 50 K, the efficiency increases to $\frac{1}{3}$. Temperatures of source and sink are respectively :

1. 300 K, 500 K
2. 500 K, 300 K
3. 375 K, 300 K
4. 300 K, 375 K

Q. A ball is projected upwards from top of tower of height of $45$ m with a speed of $40$ m/s. Find the time taken by it to reach the ground surface.

1. 3 s
2. 5 s
3. 7 s
4. 9 s

Q. A particle starts from rest and moving with an acceleration of $4{\text{ms}}^{–2}$ and covers a distance of $15\text{m}$. The final velocity of the particle will be

1. $\sqrt{120}{\text{ms}}^{-1}$
2. $\sqrt{240}{\text{ms}}^{-1}$
3. $\sqrt{360}{\text{ms}}^{-1}$
4. $\sqrt{180}{\text{ms}}^{-1}$

Q. Find the value of d(√x +1/√x) /dx

Q. A truck has an initial velocity of $50\text{m/s}$. On the application of brakes truck stops at $200\text{m}$. The acceleration of the truck will be

1. $-12.5{\text{ms}}^{-2}$
2. $24.5{\text{ms}}^{-2}$
3. $-6.25{\text{ms}}^{-2}$
4. $6.25{\text{ms}}^{-2}$

Q. An object A is released from the top of a vertical building of height $H$. At an instant when it has descended $xm$ from the top, another object B is released from $ym$ below the top of that building. Right from this instant, both these objects take the same amount of time to reach the ground. Which of the following expressions in the given situation is correct ?

1. $H=(x+y{)}^2/4x$
2. $H=(x+y{)}^2/4y$
3. $H=(x+y{)}^2/2x$
4. $H=(x+y{)}^2/2y$

Q. A particle is thrown vertically upwards. Its velocity at half of the maximum height is $20\text{m/s}$. Then the maximum height attained by it will be: (Take $g=10{\text{m/s}}^2$)

1. $40\text{m}$
2. $25\text{m}$
3. $10\text{m}$
4. $45\text{m}$

Q. A car accelerates uniformly from $20{\text{ms}}^{–1}$ to $50{\text{ms}}^{–1}$ while entering the motorway, covering a distance of $200\text{m}$. Then the acceleration of the car will be:

1. $4.25{\text{ms}}^{-2}$
2. $6.30{\text{ms}}^{-2}$
3. $5.25{\text{ms}}^{-2}$
4. $5.65{\text{ms}}^{-2}$

Q.

A charged body is kept in an electric field where it experiences a constant acceleration of 10 m/$s^2$ in the positive x-direction. The body hits wall after travelling 4 m and rebounds but can travel only upto 2 m before coming to rest momentarily . If the body was in contact with the wall for 12 ms then find the average acceleration of it due to the impact?

1. $+1.26\times {10}^{3}m/s^2$

2. $+10m/s^2$

3. $-10m/s^2$

4. $-1.26\times {10}^{3}m/s^2$

Q. A body starts from rest and moving with an acceleration $2{\text{ms}}^{–2}$. The velocity of the body when it covers a distance of $10\text{m}$ (in ${\text{ms}}^{–1}$) is

1. $\sqrt{98}$
2. $\sqrt{40}$
3. $\sqrt{20}$
4. $\sqrt{12}$

Q. The velocity acquired by a body when it falls through a height $h$ is $v$. If it further falls through a very small height $x$, the increase in velocity is approximately

1. $\frac{vx}{2h}$
2. $\frac{2vx}{h}$
3. $\frac{2v}{xh}$
4. $0.01v$

Q. 97.For the arrangement shown in the given figure, the maximum value of m , for which blocks will not accelerate is