Motion in A Str...

A particle is moving in x-y plane . At certain instant of time. The components of its velocity and acceleration are as follows $$V_x=3\ m/s$$, $$V_y = 4\ m/s$$, $${ a }_{ x }=2\ m/s^{ 2 }$$ and $${ a }_{ y }=1\ m/s^{ 2 }$$ The rate of change of speed at this moment is 

A car starts from rest and accelerates uniformly at the rate of $$ 10 cms^{-2} $$ and reaches a maximum velocity of $$72 kmph$$. it travels with this maximum velocity for some time and retards uniformly at the rate of $$ 20 cms^{-2} $$ and comes to a stop, if the total distance covered by the body is  $$ 5 km$$, find the total time of travel of the body in sec

A car is moving with a speed of $$10\,m/s$$ on a circular path of radius $$25m$$. Driver of car applies the brakes producing a uniform deceleration of $$3\,m/s^2$$. Then,

A ball is dropped from a bridge of $$122.5$$ metre above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. Initial velocity of the second ball so that both hit the water at the same time is 

A particle is moving along the x-axis whose acceleration is given a=3x-4, where x is the location of the particle. At t=0, the particle is at rest at x=4/3 m. The distance travelled by the particle is 5 s is

A stone falls freely under gravity. It covers distances  $$h _ { 1 } , h _ { 2 }$$  and  $$h _ { 3 }$$  in the first  $$5$$  seconds, the next  $$5$$ seconds and the next  $$5$$  seconds respectively. The relation between  $$h _ { 1 } , h _ { 2 }$$  and  $$h _ { 3 }$$  is

A balloon starts ascending in a vertical upward direction at a constant rate of $$5m/{s^2}$$. After $$2s$$ of its flight begins, a ball has been dropped from it, find the maximum height attained by ball. Also, calculate the position of the balloon relative to ground when ball strikes the ground. (Take g = $$10m/{s^2}$$)

A body starts from rest and travels with a uniform acceleration of $$ 3 ms^{-2} $$ and then decelerates at a uniform rate of $$ 2 ms^{-2} $$ again to come to at rest, total time of travel is $$10$$ sec. Find the maximum velocity during the journey and the total displacement

A particle starts from rest and experiences constant acceleration for 6 seconds. If it travels a distance $$d _ { 1 }$$ in the first two seconds, a distances$$d _ { 2 }$$ in the next two seconds and a distances $$d _ { 3}$$ in the last two seconds, then

An elevator ascends with an upward acceleration of $$0.2$$ $${ ms }^{ -2 }$$. At the instant its upward speed is $$2m/s$$, a loose bolt $$5$$ m high from the floor drops from the ceiling of the elevator. The time taken by the bolt to strike the floor and the distance it has fallen are