Motion in A Str...

A car starts from rest and moves in a straight line with a constant acceleration $$\alpha$$. After time $$t_0$$, brakes are applied which causes retardation of magnitude $$\beta$$ and car finally stops. The distance travelled by the car is 

A horse is running with constant acceleration $$\dfrac {g}{\sqrt {3}}$$. A small ball is projected by a horce rider at an angle $$\theta$$ with horizontal with respect to house.The value of $$\theta$$ such that the ball again caught by the boy

A lift whose cage is $$3\ m$$ high is moving up with an acceleration of $$2\ m/s^{2}$$. A piece of stone is dropped from the top of the cage of the lift when its velocity is $$8\ m/s$$. If $$g = 10\ m/s^{2}$$, then the stone will reach the floor of the lift after.

A wooden plank of mass 20kg is resting on a smooth horizontal floor. A man of mass 60kg starts moving from one end of the plank to the other end. The length of the plank is 10m. Find the displacement of the plank over the floor when the man reaches the other end of the plank.

A trolley was moving horizontally on a smooth ground with velocity $$v$$ with respect to the earth. Suddenly a man starts running from rear end of the trolley with a velocity $$\dfrac {3v}{2}$$  with respect to the trolley in opposite direction. If the length of the trolley is $$L$$, find the displacement of the man with respect to earth when he reaches the starting point on the trolley. [Mass if the trolley is equal to the mass of the man].

water drop are falling from calling at regular interval of time in such away that sixth drop if going to be deleched when $$1^{st}$$ drop it just hitting the ground. If time interval between  two consecitive drope is $$0.5$$ second. Then the height of celling it.

A force of $$50$$ $$N$$ is required to push a car on a level road with constant speed of $$10$$ $${m/s}$$. The mass of the car is $$500$$ $$kg$$. What force should be applied to make the car accelerate at $$1$$ $${m/s^2}$$?

Determine in time in which the smaller block reaches other end of bigger block in the figure.

A body moving with uniform acceleration along a straight line covers $$21\ m$$ in the fifth seconds of its motion and $$41\ m$$ in the tenth seconds of its motion. What is its initial velocity?

A car is travelling on a straight road. The maximum velocity the car can attain is $$24\ ms^{-1}$$. The maximum acceleration and deceleration it can attain are $$1\ ms^{-2}$$ and $$4\ ms^{-2}$$ respectively. The shortest time the car takes to start from rest and come to rest in a distance of $$200$$ meter is