A Particle Slides From Rest From The Topmost Point Of A Vertical Circle Of Radius R Along A Smooth Chord Making An Angle θ with The Vertical. The Time Of Descent Is

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A particle is moving along the path y = 4x2. The distance and displacement from x = 1 to x = 2 is (nearly)


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The resistive force suffered by a motor boat is αV2 where V is instantaneous velocity. The engine was shut down when the velocity of the boat was V0. Find the average velocity at any time t.


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A body sliding on a smooth inclined plane requires 5 s to reach the bottom, starting from rest at the top. How  much time does it take to cover one fourth the distance starting from rest at the top?


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Two trains, one travelling at 15 ms-1 and other at 20 ms-1, are heading towards one another along a straight track. Both the drivers apply brakes simultaneously when they are 500 m apart. If each train has a retardation of 1ms-1, the separation after they stop is


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A body is thrown vertically upward from A, the top of a tower. It reaches the ground in time t1. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time t2. If it is allowed to fall freely from A, then the time it takes the ground is given by