Motion Curves (a-t, v-t, s-t curves)

From (v-t) diagram find (1) Distance travelled in 10 second.
(2) Total distance travelled in 50 second.
(3) Retardation

Determine the speed at which the basket ball at A must be thrown at an angle 30o so that if makes it to the basket at B.
Also find at what speed it passes through the hoop.

Figure shows a collar B which moves upwards with constant velocity of 1.5 m/s.At the instant when θ=50o.Determine :
(i)The angular velocity of rod pinned at B and freely resting at A against 25o sloping ground.
(ii)The velocity of end A of the rod.

Find an expression for maximum range of a particle which is projected with an initial velocity of ‘u’ inclined at an angle of ‘β’ with the horizontal.