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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx − 2n, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by A particle of unit mass undergoes one-dimensional motion [...]

Two cars P and Q starts from a point at the same time in a straight line and their positions are represents by xp​(t) = at + bt^2 and xQ​ (t) = ft − t^2. At what time do the cars have the same velocity? if she remains stationary on the moving escalator Preeti reached [...]

(a) Show that the velocity acquired by a particle in sliding down an inclined plane is the same as that acquired by a particle falling freely from rest through a distance equal to the height of the inclined plane. (b) Find the time taken in sliding a particle down the whole length of the incline. [...]

If the velocity of a particle is v = At + Bt^2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is If the velocity of a particle is v = At + Bt^2 then the distance travelled by it between 1 s and 2 s [...]

A balloon starts rising upwards with constant acceleration a and after time t 0 ​ second, a packet is dropped from it which it reaches the ground after t seconds of dropping. Determine the value of t A balloon starts rising upwards with constant acceleration a and after time t 0 ​ second a packet [...]

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1​. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2​. The time taken by her walk up on the moving escalator will be: [...]

From a point A, 80 m above the ground, a particle is projected vertically upwards with a velocity of 29 .4. m s^(-1), Five seconds later, another particle is dropped from a point B, 34. 3 m vertically below A Derermine when and where one voertakes the other. Take g=9.8 m s^(-2). 34. 3 m [...]

A body is projected upwards with a velocity u. It passes through a certain point above the grond after t_(1), Find the time after which the body posses thoruth the same point during the journey. A body is projected upwards with a velocity u. It passes through a certain point above the grond after t_(1) [...]

A body is thrown vertically upwards from the top A of a tower. It reaches the ground in t 1 ​ seconds. If it thrown vertically downwards from A with same speed it reaches the ground in t 2 ​ seconds. If it is allowed to fall freely from A, then the time it takes [...]

Two particles 1 and 2 are projected simultaneously with velocities v 1 ​ and v 2 ​ , respectively. Particle 1 is projected vertically up from the top of a cliff of height h and particle 2 is projected vertically up from the bottom of the cliff. Find the time of meeting of particles, if [...]