Motion in A Str...

Which of the following equations represents the motion of a body moving with constant finite acceleration? in these equations, $$y$$ denote the displacement in time $$t$$ and $$p, q$$ and $$r$$ are arbitary constants:

A body is projected vertically upwards with speed $$40 m/s$$ . The distance traveled by the body in the last second of upward journey is ( take  g= $$9.8 m/s^2$$ and neglect effect of air resistance)

A trolley is moving horizontally with a constant velocity of v m/s w.r.t. earth. A man starts running from one end of the trolley with a velocity $$1.5v m/s$$ w.r.t. to trolley. After reaching the opposite end, the man return back to starting end and continues running with a velocity of 1.5 v m/s w.r.t. the trolley in the backward direction. If the length of the trolley is L then the displacement of the man with respect to earth during the process will be :

A body is thrown vertically upwards and takes 5 seconds to reach maximum height. the distance travelled by the body will be same in 

A taxi leaves the station $$X$$ for station $$Y$$ every $$10$$ minutes. Simultaneously, a taxi also leaves the station $$Y$$ for station $$X$$ every $$10$$ minutes. The taxies move at the same constant speed and go from $$X$$ to $$Y$$ or vice versa in $$2$$ hours. How many taxies coming from the other side will meet each taxi in route from $$Y$$ to $$X$$?

Two cars are moving in the same directions with the same speed of $$30$$ km/hr. They are separated by $$5$$ km. What is the speed of the car moving in the opposite direction if it meets the second cars at an interval of $$4$$ minute?

A particle moves in a straight line with a constant acceleration. it changes its velocity from $$10\ ms^{-1}$$ to $$20\ ms^{-1}$$ while passing through a distance $$135\ m$$ in $$t$$ seconds. The value of $$t$$ is

A particle starts from rest with constant acceleration for 20 s. If it travels a distance $$y_1$$ in the first 10 s and a distance $$y_2$$ in the next 10 s then

A body is allowed to slide from the top along a smooth inclined plane of length 5m at an angle of inclination $$30^o$$. If $$g = 10ms^{-2}$$, time taken by the body to reach the bottom of the plane is

A parachutist after bailing out falls for $$10s$$ without friction. When the parachute opens he descends with an acceleration of $$2\ m/s^{2}$$ against his direction and reached the ground with $4\ m/s$. From what height he has dropped himself? $$(g=10m/s^{2})$$