Question 1 :
Four persons K, L, M and N are initially at rest at four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N and N directly towards K. Show that the four persons will meet at time t = <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5ce4389b1556ddf0044' height='109' width='122' >

Question 2 :
Blocks <em>A</em> and <em>C</em> start from rest and move as shown with acceleration <em>a</em>_<em>A</em> = 12<em>t</em> m/s² and <em>a</em>_<em>C</em>=3 m/s². Here <em>t</em> is in seconds. The time when block <em>B</em> again comes to rest is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd6b1da6d070c2abf840"/>

Question 3 :
A particle starts from the origin at {tex} t = 0 {/tex} s with a velocity of {tex} 10.0 \hat { j } \mathrm { m } / \mathrm { s } {/tex} and moves in the {tex} x - y {/tex} plane with a constant acceleration of {tex} ( 8.0 \hat { i } + 2.0 \hat { j } ) \mathrm { ms } ^ { - 2 } {/tex} At a time when {tex} x {/tex} -coordinate of the particle {tex} 16 \mathrm { m } , {/tex}What is the y-coordinate of the particle at that time?

Question 4 :
A body of mass 1 kg starts moving from rest at t = 0, in a circular path of radius 8 m. Its kinetic energy varies as a function of time as KE = 2t² J, where t is in seconds. Then -

Question 5 :
{tex}\mathrm {Assertion} \quad {/tex} :An object can have constant speed but variable velocity.<br> {tex}\mathrm {Reason} \quad {/tex} :Speed is a scalar but velocity is a vector quantity.

Question 6 :
A particle is moving eastwards with a velocity of {tex} 5 \mathrm { m } / \mathrm { s } {/tex}. In {tex} 10 \mathrm { s } {/tex} the velocity changes to {tex} 5 \mathrm { m } / \mathrm { s } {/tex} northwards. The average acceleration in this time is (a) zero

Question 7 :
A body is in rectilinear motion with an acceleration given by {tex} a = 2 v ^ { 3 / 2 } {/tex} . If particle starts its motion from origin with a velocity of 4{tex} \mathrm { ms } ^ { - 1 } {/tex} , the position {tex} x {/tex} of the particle at an instant in terms of {tex} v {/tex} can be given as

Question 8 :
Two bodies are thrown simultaneously from a tower with same initial velocity {tex} v _ { 0 }: {/tex} one vertically upwards, the other vertically downwards. The distance between the two bodies after time {tex} t {/tex} is

Question 9 :
The angle which the velocity vector of a projectile thrown with a velocity {tex} v {/tex} at angle {tex} \theta {/tex} to the horizontal will make with the horizontal after time {tex} t {/tex} of its being thrown up is

Question 10 :
An aeroplane flying horizontally with a speed of 360 km^-1 releases a bomb at a height of 490 m from the ground. If g = 9.8 m s^-2, it will strike the ground at