Equations of Motion

Q. A rocket is moving in a gravity-free space with a constant acceleration of $2{\text{ms}}^{-2}$ along$+x$ direction (see figure). The length of a chamber inside the rocket is $4\text{m}$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3{\text{ms}}^{-1}$ relative to the rocket. At the same time. Another ball is thrown in $-x$ direction with a speed of $0.2{\text{ms}}^{-1}$ from its right end relative to the rocket. The time in $\text{seconds}$ when the two balls hit each other is (nearest integer)

Q.

A mass of 10 gm moving with a velocity of 100 cm/s strikes a pendulum bob of mass 10 gm. The two masses stick together. The maximum height reached by the system now is $(g=10m/s^2)$

1. Zero

2. 1.25 cm

3. 5 cm

4. 2.5 cm

Q. A body of mass 0.40 kg moving initially with a constant speed of 10 m s-1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.

Q.

If we throw a body upwards with velocity of $4m{s}^{-1}$ at what height its kinetic energy reduces to half its initial value ? Take $g=10m/s^2$

1. 4m

2. 2m

3. 0.4 m

4. 1m

Q. The relation between position(x) and time (t) are given below for a particle moving along a straight line.Which of the following equation represents uniformly accelerated motion ? \lbrack where α and β are positive cons†an ts\rbrack (1)β x=α t+αβ (2)α x=β+t (3)xt=αβ (4)α t=root β+x ​ ​

Q. 136.A bullet leaves the barrel of a rifle with a speed of 300m/s. If the length of the barrel is 0.9 m, at what rate is the bullet accelerated while in the barrel?

Q. A person rows his boat in stream with a speed of 2m/s. ater in the stream is flowing perpendicular to the direction of flow, find graphically his resul†an t velocity.

Q. How to derive the equations of motion 1. v= u + at 2. s= ut + 1/2at^2 3. v^{2 }- u^2 = 2a

Q. a ball is projected vertically upwards from ground with velocity 12m/s in the presence of air drag whose magnitudevalways remains cons†an t .if ball takes one second to the highest point in presenceof air friction then calculate the difference of time of flight of ball in presence of and in absence of air friction

Q. Starting from rest a car accelerates at a constant rate alpha and then retards at a constant rate bita to come to stop if the total time of motion is t. Find (i) Maximum velocity of car. (ii)Total distance travelled by the car.

Q. A car, having acceleration $1m{s}^{-2}$, is moving with an initial velocity $10m/s$ and it stops after 10 seconds as the driver applied brakes. Find the distance travelled by the car.

1. 30 m
2. 50 m
3. 60 m
4. 40 m

Q. A projectile of mass $m$ is fired with a velocity $u$ from a point $P$ as shown. Neglecting air resistance, find the magnitude of the change in momentum of the projectile between the points $P$ and $Q$.

1. $mu\sec \beta \sin (\alpha -\beta )$
2. $mu\sin \alpha (\tan \beta -1)$
3. $mu(\tan \beta -1)$
4. $mu\cos \alpha$

Q.

A body is executing S.H.M. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

1. 2π sec

2. π/2 sec

3. π sec

4. 3π/2 sec

Q. An elevator and its load have a total mass of $800\text{kg}$. If the elevator, originally moving downward at $10\text{m/s}$, is brought to rest with constant deceleration in a distance of $25\text{m}$, the tension in the supporting cable will be ($g=10{\text{m/s}}^2$)

1. $8000\text{N}$
2. $6500\text{N}$
3. $11200\text{N}$
4. $9600\text{N}$

Q. A person driving a car with speed 72 km/h suddenly sees a boy crossing the road.If the distance moved by the car before the person applies brakes is 5m.Then reaction time of person is}(1) 0.5s(2) 0.10s(3) 10s(4) 0.25

Q. A stone weighing $3\text{kg}$ falls from the top of a tower $100\text{m}$ high and buries itself $2\text{m}$ deep in sand. Find the time (in seconds) of penetration $(g=10{\text{m/s}}^2)$

1. $\sqrt{5}$
2. $2\sqrt{5}$
3. $25\sqrt{5}$
4. $\frac{1}{5\sqrt{5}}$

Q. A train has each compartment of mass $‘m^{\prime }$ is accelerating uniformly. The velocity of the engine is $V_1$ and the velocity of the last compartment is $V_2$. Find the velocity of the compartment in the middle when it passes the same mile marker assuming that the compartments are of point sizes.

1. $\sqrt{\frac{V_1^2-V_2^2}{2}}$
2. $\sqrt{\frac{V_1^2+V_2^2}{2}}$
3. $\frac{V_1^2-V_2^2}{2}$
4. $\frac{V_1^2+V_2^2}{2}$

Q. A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m s-1. How long does the body take to stop ?

Q. A body of mass $10\text{kg}$ is moving with a constant velocity $10\text{m/s}$. When a constant force acts for $4\text{s}$ on it, it moves with a velocity $2\text{m/s}$ in the opposite direction. The magnitude of force acting on the body is

1. $10\text{N}$
2. $30\text{N}$
3. $45\text{N}$
4. $50\text{N}$

Q. A body of mass $2kg$ has an initial speed of $5m/s$. A force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. The final speed of the body is

1. $9.25m/s$
2. $5m/s$
3. $14.25m/s$
4. $4.25m/s$

Q. Choose the correct statements among the following options.

1. The area under the force time graph gives impulse
2. The rate of change of momentum of body is directly proportional to the applied force
3. All of these
4. The area under the force time graph gives change in momentum

Q. A truck starts from rest and accelerates uniformly at 2.0 m s¯². At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 11s ? (Neglect air resistance.)

Q. Increase in KE of a car E1 when it is accelerated from 15 m/s to 20 m/s and increase in KE of a car is E2 when it is accelerated from 20 m/s to 25 m/s . Find E1/E2 .

Q. A body of mass $5\text{kg}$ is moving along a straight line with a velocity of $2{\text{ms}}^{-1}$. A variable force $F$ started acting on it for a time period of $0.5s$ as shown in force - time curve. The final velocity of the block is

1. $2{\text{ms}}^{-1}$
2. $2.2{\text{ms}}^{-1}$
3. $2.5{\text{ms}}^{-1}$
4. $2.7{\text{ms}}^{-1}$

Q. A force acts for 10 sec on a body of mass $100\text{kg}$ after which it ceases. If the body travels $160\text{m}$ in the next 8 sec, find the magnitude of the force.

1. $100\text{N}$
2. $200\text{N}$
3. $300\text{N}$
4. $400\text{N}$

Q. A body of mass $1kg$ is subjected to a force of $20N$ for $10$ seconds after which the force ceases to act. What distance would it travel in the next $10$ seconds? Assume that the body starts from rest.

1. $20m$
2. $200m$
3. $2km$
4. $20km$

Q. A body of mass $1kg$ is traveling with a velocity of $3m/s$ accelerates uniformly to acquire a velocity of $8m/s$ in $2s$. Find the force acting on the body.

1. $3\text{N}$
2. $2\text{N}$
3. $2.5\text{N}$
4. $5\text{N}$

Q. A stone weighing $3kg$ falls from the top of a tower $100m$ high and buries itself $2m$ deep in sand. Find the time (in seconds) of penetration $(g=10m/s^2)$

1. $\sqrt{5}$
2. $2\sqrt{5}$
3. $25\sqrt{5}$
4. $\frac{\sqrt{5}}{25}$

Q. In a projectile motion let $v_x$ and $v_y$ be the horizontal and vertical components of velocity at any time $t$ and $x$ and $y$ be the displacements along horizontal and vertical from the point of projection at any time $t$. Then

1. $v_y-t$ graph is a straight line with negative slope and positive intercept.
2. $x-t$ graph is a straight line passing through origin.
3. $y-t$ graph is a straight line passing through origin.
4. $v_x-t$ graph is a straight line parallel to $t-$ axis.

Q. A rigid ball of mass $m$ strikes a rigid wall at ${60}^{\circ }$ and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

1. $mV$
2. $2mV$
3. $\frac{mV}{2}$
4. $\frac{mV}{3}$