Question 1 :
Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km $h^{-1}$ in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service is

Question 2 :
A ball is thrown from a point with a speed {tex} v _ { 0 } {/tex} at an angle of projection {tex} \theta . {/tex} From the same point and at the same instant a person starts running with a constant speed {tex} v _ { 0 } / 2 {/tex} to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

Question 3 :
An object is projected with velocity $20m{s}^{-1}$ making an angle of ${45}^{o}$ with horizontal. The equation for its trajectory is $h=Ax-B{x}^{2}$ where $h$ is the height and $x$ the horizontal distance at any instant. The ratio of constants A:B is

Question 4 :
A train moves from one station to another in 2 hours time. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is <br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ec26171d478eb6a39d86c31' class="uploaded-image" />

Question 5 :
A ball is thrown from the ground to clear a wall <b>3 m</b> high at a distance of <b>6 m</b> and falls <b>18 m</b> away from the wall, the angle of projection of ball is

Question 6 :
A girl standing on a pedstal at rest throws a ball upwards with maximum possible speed of 50 ms^-1. If the platform starts moving up at 5 ms^-1 and the girl again throws the similar ball in similar way. The time taken in the previous case and the time taken in the second case to return to her hands are

Question 7 :
In a harbour, wind is blowing at the speed of {tex}72 \mathrm { km } / \mathrm { h } {/tex} and the flag on the mast of a boat anchored in the harbour flutters along the {tex} \mathrm { N } - \mathrm { E } {/tex} direction. If the boat starts moving at a speed of {tex}51 \mathrm { km } / \mathrm { h } {/tex} to the north, what is the direction of the flag on the mast of the boat?

Question 8 :
Which of the following statement is true if a body moves in a semicircular track whose radius is R: (a) 2R is the displacement of the body (b) {tex} \pi {/tex}R is the distance traveled by the body (c) Both (a) and (b) are correct (d) None of the above

Question 9 :
A stone is dropped into water from a bridge {tex} 44.1 \mathrm { m } {/tex} above the water. Another stone is thrown vertically downward 1 sec later. Both strike the water simultaneously. What was the initial speed of the second stone

Question 10 :
A train is travelling at a speed of $108\ km/h$. Brakes are applied so as to produce a uniform retardation of $1\ m/s^{2}$. Find how far the train will go before it is brought to rest :

Question 11 :
A stone tied to the end of a string 80{tex} \mathrm { cm } {/tex} long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25{tex} \mathrm { s } {/tex} , what is the magnitude of acceleration of the stone?

Question 12 :
A cannon shell is fired straight up from the ground at an initial speed of $225 m/s$. After how much time is the shell at a height of $6.20 * 10^{2} m$ above the ground and moving downward?<br>

Question 13 :
An object is dropped from a height $h$ from the ground. Every time it hits the ground it looses $50\%$ of its kinetic energy. The total distance covered at $ t\rightarrow \infty$ is

Question 14 :
A projectile is fired vertically upwards with an initial velocity {tex} u {/tex} . After an interval of {tex} T {/tex} seconds a second projectile is fired vertically upwards, also with initial velocity {tex} u {/tex} . The correct statement is

Question 15 :
A man standing on the roof of a house of height {tex} h {/tex} throws one particle vertically downwards and another particle horizontally with the same velocity {tex} u . {/tex} The ratio of their velocities when they reach the earth's surface will be

Question 16 :
A particle starts from rest and moves with uniform acceleration. If covers a displacement of $y^{2}-x^{2}$ in the first $10\ sec$ and $y^{2}+x^{2}$ in the next first $10\ sec$, then

Question 17 :
A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will

Question 18 :
A point particle starting from rest has a velocity that increases linearly with time such that $v=pt$ where $p=4m/s^2$. The distance covered in the first $2$ sec will be?

Question 19 :
The maximum height attained by a projectile is increased by {tex} 5 \% , {/tex} keeping the angle of projection constant. The corresponding percentage increase in horizontal range will be

Question 20 :
A particle is projected with a velocity <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e57cb5f89758f2d4ef30' height='23' width='45' >, 3m away from a vertical wall. After striking the wall it lands at ............... away from the wall B

Question 21 :
On a long horizontally moving belt, a child runs to and fro with a speed 9 km h^-1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h^-1. For an observer on a stationary platform outside, what is the time taken by the child to go from father to mother and back to father is

Question 22 :
Journey in a train is adventurous particularly when you have a seat. The girl sitting near window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically down and touched the ground in $0.2s$. After sometime she requested her sister sitting on the upper berth to drop a chocolate bar.The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train is accelerating it did not reach you and fell in front of you. An observer standing outside the train finds the banana peel moving<br/>

Question 23 :
Two trains {tex} A {/tex} and {tex} B {/tex} are moving on same track in opposite direction with velocity {tex}25 \mathrm { m } / \mathrm { s } {/tex} and {tex}15 \mathrm { m } / \mathrm { s } {/tex} respectively. When separation between them becomes {tex} 225 \mathrm { m } , {/tex} drivers of both the trains apply brakes producing uniform retardation in train {tex} A {/tex} while retardation of train {tex} B {/tex} increases linearly with time at the rate of {tex} 0.3 \mathrm { m } / \mathrm { s } ^ { 3 } . {/tex} The minimum retardation of train {tex} A {/tex} to avoid collision will be

Question 24 :
A car moves of a circular track of radius $\dfrac{7}{22}$ km. After its start, when its displacement becomes zero for the first time, the distance covered by the car is

Question 25 :
Find the radius of curvature of a projectile at the highest point, fired with a velocity v, making an angle &theta; with the horizontal.

Question 26 :
A particle is moving in a straight line and passes through a point {tex} O {/tex} with a velocity of {tex} 6 \mathrm { ms } ^ { - 1 } {/tex}. The particle moves with a constant retardation of {tex} 2 \mathrm { ms } ^ { - 2 } {/tex} for {tex} 4 s {/tex} and there after moves with constant velocity. How long after leaving {tex} O {/tex} does the particle return to {tex} \mathrm { O } {/tex}

Question 27 :
A car starts from rest moving along a line, first with acceleration a= $2 m/s^{2}$ , then uniformly and finally decelerating at the same rate and comes to rest. The total time of motion is $10$ sec. The average speed during this time is $3.2 m/s$. How long does the car move uniformly?(in seconds)

Question 28 :
A particle is projected with a velocity {tex} v {/tex} such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where {tex} g {/tex} is acceleration due to gravity)

Question 29 :
<p>The displacement of a particle moving in a straight line is described by the relation, $s = 6 + 12t - 2t^2$.Here $s$ is in metre and $t$ in second. The distance covered by the particle in first 5 s is</p>

Question 30 :
A cannon on a level plane is aimed at an angle $\theta $ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards a vertical cliff a distance $D$ away.Then the height from the bottom at which the shell strikes the side wall of the cliff is