The instantaneous velocity of a particle moving in a straight line is given as $$V = \alpha t + \beta {t^2}$$, where $$\alpha$$ and $$\beta$$ are constants. The distance travelled by the particle between 1s and 2s is :

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4^th second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = 9.8 m/s²)

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t₁. If he remains stationary on a moving escalator then the escalator takes him up in time t₂. The time taken by him to walk up on the moving escalator will be :

The velocity $$-$$ displacement graph of a particle is shown in the figure.


The acceleration $$-$$ displacement graph of the same particle is represented by :