114 - Kinematics Questions Answers

a particle is moving along a straight line such that its position varies with time t as x=6α [ t+ αsin (t/α) 

where x is its position in metre, t is time in s and α is a positive constant 

The particle comes to rest at time t = (in terms of α and π)

a vector a which has magnitude 8 is added to a vector B which lies on x-axis. The sum of these two vectors, lies on y-axis and has a magnitude twice of the magnitude of B. The magnitude of vector B is

the forces F₁ and F₂ are acting perpendicular to each other at a point and have resultant R. If force F2 is replaced by R² - F₁²/F₂ acting in the direction opposite to that of F₂, the magnitude of resultant

A sleeping cat and a sleeping dog are initially at a distance 'l' metres. As soon as the dog wakes up, the cat runs in the horizontal direction with constant velocity of u m/s. Immediately the dog chases the cat with constant speed of v m/s. Initially the dog was facing the north direction towards cat. The cat starts running in the east direction. Assuming the dog aims at the cat with constant speed v m/s, find the time after which the dog chases the cat.

Time of flight of a projectile thrown from ground is 8√5 s. It will rise up to a height of.........

A projectile is projected with velocity u= ai+bj from ground if acceleration due ti gravity is g, then the change in velocity of the projectile in second of projection is

A shell at rest at large height explodes into two parts which move horizontally with speeds v¹ and v². After what time their instantaneous velocities are perpendicular?

A particle moving in uniform circular motion undergoes an angular displacement α (less then 360°) from point P and Q. Then angle between average velocity from P to Q and velocity at Q is........

A particle moves in the plane xy with velocity v = ai + bxj, where i and j are the unit vectors of the x and y axes, and a and b are constants. At the initial moment of time the particle was located at the point x = y = 0. Find: 
(a) the equation of the particle's trajectory y(x); 
(b) the curvature radius of trajectory as a function of x. 

A ball is thrown up with some velocity after time t second it is at height h from the ground which is given by h = at -1/2 bt². The dh/dt is zero at t equal to