Question 1 : The co-ordinates of a particle restricted to move in a plane is given by<br/>$X = 6\ cos\pi t$<br/>$y= 1-4cos2\ \pi t$<br/>The magnitude of acceleration of particle at $t=1.5\ s$ is (where $x$ and $y$ are in meter and $t$ is in seconds)<br/><br/>

Question 3 : The displacement of a particle varies with time as $x=a e^{-\alpha t}+b e^{\beta t }$ where $a,\alpha ,b,\beta $ are positive constants. The velocity of the particle&#160;will&#160;<br/>

Question 4 : A car of mas sm starts moving so that its velocity varies according to the law $v = \beta\, \sqrt{s}$ where $\beta$ is a constant, ands is the distance covered. The total work performed by all the forces which are acting on the car during the first t seconds after the beginning of motion is

Question 5 : Displacement $(x)$ of a particle is related to time $(t)$ as $x = at + bt^{2} +ct^{3}$ where $a, b$ and $c$ are constants of motion. The velocity of the particle when its acceleration is zero, is given by:

Question 6 : A&#160;body is thrown vertically upwards and rises&#160;to a height&#160;of 10 m. The time taken by the&#160;body to reach the highest point is :

Question 7 : In above que. find the condition when bobbin moves to left :<br/>

Question 8 : Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity u and the second starts from rest with constant acceleration f. Then<br>

Question 9 : A ball is thrown vertically upwards. It was observed at a height h twice with a time interval $ \Delta t $ . The initial velocity of the ball is

Question 10 : Two cars $A$ and $B$ are travelling in the same direction with velocities ${ v }_{ A }$ and ${ v }_{ B } \left( { v }_{ A }&gt;{ v }_{ B } \right)$. When the car $A$ is at a distance $d$ behind the car $B$ the driver of the car $A$ applies brakes producing a uniform retardation $a$. There will be no collision when

Question 11 : Two cars moving in the same direction with a speed of&#160;$\displaystyle 30\ km{ h }^{ -1 }$. They are separated from each other by $5\ km$. Third car moving in the opposite direction meets the two cars after an interval of $4\ min$. What is the speed of third car?

Question 12 : &#160;A truck and a car are moving with equal velocity; on applying brakes, both will stop after a certain distance, then:&#160;

Question 13 : A proton and an $\alpha-$particle enter a uniform magnetic field perpendicular with the same speed. If proton takes $20\mu s$ to make $5$ revolution, then the periodic time for the $\alpha-$particle would be:<br/>

Question 14 : The coefficient of kinetic friction between the road and the tyres is $0.2$. Then the shortest distance in which a car be stopped if it was travelling with a velocity of $72$ kmph is ( g = 9.8 $ms^{-2}$)

Question 15 : A body is in motion and it is stopped by applying retarding force. Initial speed and magnitude of force applied are as given below :<br/><table class="wysiwyg-table"><tbody><tr><td>Speed</td><td>Force</td></tr><tr><td>V</td><td>F</td></tr><tr><td>2V</td><td>F/2</td></tr><tr><td>V/2</td><td>2F</td></tr></tbody></table><br/>If&#160;$S_{1}$, $S_{2}$,&#160;$S_{3}$&#160;are the distance travelled before coming to rest, those can be arranged in ascending order as given below

Question 17 : A train is running at 5 m/s and a man jumps out of it with a velocity 10 m/s in a direction making an angle of 60$^o$ with the direction of the train. The velocity of the man relative to the ground is equal to

Question 18 : Two particles one with constant velocity $50\ m/s$ and the other with uniform acceleration $10\ m/ s^{2}$,&#160;start moving simultaneously from the same place&#160;in the same direction. They will be at a distance of $125\ m$ from each other after

Question 19 : Determine her average velocities in (in $m/s$)&#160;the second half of the swim.

Question 20 : A bullet on penetrating $30\ cm$ into its target loses its velocity by $50$%. What additional distance will it penetrate into the target before it comes to rest?

Question 21 : A bus moving on a level road with a velocity $V$ can be stopped at a distance of $x$, by the application of a retarding force $F$. The load on the bus is increased by $25\%$ by boarding the passengers. Now, if the bus is moving with the same speed and if the same retarding force is applied, the distance travelled by the bus before it stops is:

Question 22 : A driver applies brakes when he sees a child on the railway track, the speed of the train reduces from 54 km $h^{-1}$ to 18 km $h^{-1}$ in 5 s. What is the distance travelled by the train during this interval of time?

Question 23 : A boy throws a ball to his friend 20 m away. The ball reaches to his friend in 4 s. The friend then throws the ball back to the boy and it reaches the boy in 5 s. Assume the ball travels with constant velocity during any throw. For the entire motion

Question 24 : The acceleration $a$ (in ${ ms }^{ -2 }$) of a body, starting from rest varies with time $t$ (in $s$) following the equation $a=3t+4$. The velocity of the body at time $t=2s$ will be

Question 25 : what is the velocity of a monkey running on the roof of the train A ( moving with velocity $54 \ kh/hr$) against its motion with a velocity of 18 km $h^{-1}$ with respect to the train A as observed by a man standing on the ground?

Question 26 : When a train is stopped by applying break it stops after travelling a distance of $50\ m$. If speed of train is doubled and same retarding force is applied then it stops after travelling a distance of:

Question 27 : A lift is coming from 8th floor and is just about to reach&#160;4th floor. Taking ground floor as origin and positive&#160;direction upwards for all quantities, which one of the&#160;following is correct?<br/>

Question 28 : A gun is fired at a target. At the moment of firing, the target is released and allowed to fall freely under gravity. Then the bullet :<br/>(Assume zero air resistance)

Question 29 : A bus begins to move with an acceleration of $\dfrac{1}{2} \,m/s^2$. A person who is $40 \,m$ behind the bus, runs at a rate of $7 \,m/s$. Find the time taken by the person to catch the bus.

Question 30 : Two bodies are projected simultaneously from the same point, in the same vertical plane, one towards east and other towards west with velocities $8ms^{-1}$and $2ms^{-1}$&#160;respectively. The time at which their velocities are perpendicular to each other is

Question 31 : At a particular height, the velocity of an ascending body is $\vec { u } $. The velocity at the same height while the body falls freely is

Question 32 : <p>A particle moves in a straight line in such a way that its velocity at any point is given by $v^2 = 2 -3x$, where $x$ is measured from a fixed point. The acceleration is :</p>

Question 33 : Starting from rest, when a body moves with uniform acceleration, then distances covered after 1st, 2nd, 3rd, ... seconds are in the ratio

Question 34 : A boy throws balls into air at regular interval of $2$ second. The next ball is thrown when the velocity of first ball is zero. How high do the ball rise above his hand? [Take $g = 9.8\ m/s^{2}]$.

Question 35 : The function which represents the height, $h(t)$, of a ball t seconds after it is kicked into the air is<br/>$h(t)\, =\, - 16t^2\, +\, 64t$.<br/>What does $t$ represent if $h(t)$ is zero ?

Question 36 : The maximum separation between the floor of elevator and the ball during its flight would be <br>

Question 37 : Two particles $P$ and $Q$ move in a straight line $AB$ towards each other. $P$ starts from $A$ with&#160;velocity $u_{1}$,&#160;and an acceleration $a_{1}$, $Q$ starts&#160;from $B$ with velocity $u_{2}$&#160;and acceleration $a_{2}$.They pass each other at the midpoint of $AB$ and arrive at the other ends of $AB$ with equal&#160;<i></i>velocities

Question 38 : Displacement of ball with respect to ground during its flight would be<br>

Question 39 : A man is driving at the speed $40 mph$ when he see an obstacle at distance $300 ft$ ahead of his position. The driver applies the brakes and decelerates at $10 ft/s^2$.How far from the obstacle will the driver be when he finally stops? (in metres)

Question 40 : A particle starts from the origin with a velocity of 10 m/s and moves with a constant acceleration till the velocity increases to 50 m/s. At that instant, the acceleration is suddenly reversed. What will be the velocity of the particle, when it returns to the starting point?