Kinematics(Motion in a straight line with constant acceleration)(Problems)

1). The position of a particle along the x-axis is given by 9.75+1.5t³. Find:

(          a)    Average velocity between t=2 and t=3 seconds.

           b)   Instantaneous velocity at t=2 seconds.

           c)    Instantaneous velocity at t=2.5 seconds.

2). A motorcyclist moving with uniform retardation takes 10 sec and 20 sec respectively to travel
     successive quarter km. How much further will he travel before coming to rest?

3). A point moving in a straight line traversed half the distance with a velocity v₀. The remaining part of the
     distance was covered with velocity v₁ for half the time, and with velocity v₂ for the other half of the
     time. Find the mean velocity of the point averaged over the whole time of motion.
4).At the instant a traffic light turns green, a car starts with a constant acceleration of 2.2 m/s². At the same
    instant a truck, travelling with a constant speed of 9.5 m/s² overtakes and passes the car.
    (a) How far beyond the starting point will the car overtake the truck?

    (b) How fast will the car be travelling at the instant?

5).A train is crossing an observer standing on a platform. The first compartment of the train takes 2 sec to
    cross the observer while the second compartment of the train takes 2.5 sec to cross him. The train is
    moving with uniform acceleration. Find

    (a) Velocity of the train when the front of the first compartment crosses the observer.

    (b) The acceleration of the train

    (The length of each compartment is 15 m.)