Motion in A Str...

Two points $$A$$ and $$B$$ move from rest along a straight line with same acceleration $$f$$ and $$f'$$ respectively. If  $$A$$ takes $$m\ \text{sec}$$ more than $$B$$ and describes $$n$$ units more than $$B$$ in acquiring the same speed then 

A lizard, at an initial distance of $$21$$ cm behind an insect, moves from rest with an
acceleration of $$2 cm/s^{2}$$ and pursues the insect which is crawling uniformly along a
straight line at a speed of $$20$$ cm/s. Then the lizard will catch the insect after 

Two stones are thrown up simultaneously from the edge of a cliff $$240\ m$$ high with initial speed $$10\ m/s$$ and $$40\ m/s$$ respectively.  Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take $$g = 10\ m /s^2$$)
(The figures are schematic and not drawn to scale.)

STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $$\overrightarrow{E}$$. Due to the force $$q\overrightarrow{E}$$, its velocity increases from $$0$$ to $$6\ m/s$$ in one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $$0$$ to $$3$$ seconds are respectively:

A ball is dropped from a bridge $$122.5 m$$ high. After the first ball has fallen for $$2 seconds$$, a second ball is thrown straight down after it, what must be the initial velocity of the second ball be, so that both the balls hit the surface of water at the same time?

If a car at rest accelerated uniformly to a speed of $$144  {km}/{hour}$$ in $$20 second$$ it covers a distance:

A particle of mass $$2\ m$$ is projected at an angle $$45^{\circ}$$ with the horizontal with a velocity of $$20\sqrt {2}m/ s$$. After $$1s$$, explosion takes place and the particle is broken into the two equal pieces. As a result of explosion, one part comes to rest. The maximum height from the ground attained by the other part is

A ball is thrown vertically upwards with a given velocity such that it rises for T seconds (T > 1). What is the distance traversed by the ball during the last one second of ascent (in meters) ? (Acceleration due to gravity is g $$m/s^{2}$$ ) .

A body starts from rest and acquires a velocity $$10m s^{-1}$$  in 2 s. Find the acceleration.