The `XI^(th)` class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At `t = 0`, the rocket is at `y = 0` with `V_(y) (t = 0) = 0`. The velocity of the rocket is given by: `V_(y) = (24t - 3t^(2))m//s` for `0 le t le t_(b)` where `t_(b)` is the time at which fuel burns out. vertically upward direction is taken as positive. `(g = 10m//s^(2))`
The time taken for rocket to reach its maximum height is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The displacement of the rocket till the fuel burns out (t = t_(b)) is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The displacement of the rocket till the fuel burns out (t = t_(b)) is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The displacement of the rocket till the fuel burns out (t = t_(b)) is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The expression for the acceleration a_(y)(t) valid at all times in the interval 0 lt t lt t_(b) is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The expression for the acceleration a_(y)(t) valid at all times in the interval 0 lt t lt t_(b) is

The XI^(th) class students of ALLEN designed a rocket. The rocket was launched from cycle stand of ALLEN straight up into the air. At t = 0 , the rocket is at y = 0 with V_(y) (t = 0) = 0 . The velocity of the rocket is given by: V_(y) = (24t - 3t^(2))m//s for 0 le t le t_(b) where t_(b) is the time at which fuel burns out. vertically upward direction is taken as positive. (g = 10m//s^(2)) The expression for the acceleration a_(y)(t) valid at all times in the interval 0 lt t lt t_(b) is

The velocity of particle at time t is given by the relation v=6t-(t^(2))/(6) . The distance traveled in 3 s is, if s=0 at t=0

A model rocket is launched from the ground. The height 'h' reached by the rocket after t seconds from lift off is given by h(t) = - 5t^(2) + 100t, 0 le t le 20 . At what time the rocket is 495 feet above the ground?

The velocity of a particle is given by v=v_(0) sin omegat , where v_(0) is constant and omega=2pi//T . Find the average velocity in time interval t=0 to t=T//2.

A rocket prototype is fired from ground at time t = 0 and it goes straight up. Take the launch point as origin and vertically upward direction as positive x direction. The acceleration of the rocket is given by a = (g)/(2) - kt^(2), 0 lt t le t_(0) =- g, t gt t_(0) Where t_(0) = sqrt((3g)/(2k)) (a) Find maximum velocity of the rocket during the up journey. (b) Find maximum height attained by the rocket. (c) Find total time of flight.