Problems Kinematics Basics - I

Problems From the top of a tower a ball is thrown up and reaches the ground at time t1. Another ball with same speed is thrown down and reaches ground at time t2. Another ball is dropped from the tower and reaches ground at time t3. Find the relation between t1, t2 and t3 (Ans : t3= Sqrt( t1 t2) ) A balloon starts rising from the ground with acceleration of 1.25m/s^2. After 8 secs, a stone is released from the balloon. The time it takes the stone to reach ground is__ sec. (Ans 4 sec). A hollow vertical cylinder of radius r and height h has a smooth internal surface. A small particle is placed in contact with the inner side and given a horizontal velocity u m/s. Find the number of revolutions the particles made before finally appearing out of the other end. For the above figure which of the following is true Particle changes its direction of motion at some point? The acceleration of particle remains constant? The displacement of particle is zero? The initial and final speeds of the particle are same? A particle moves with an initial velocity V0 and retardation V where V is its velocity at any time t. Which of the following is true? Particle will cover a total distance of V0/. Particle will come to rest after time t=1/. Particle will continue to move for a very long time. Velocity of the particle will become V0/2 after time t= 1/. Consider the Pulley System as below: What is the velocity V of block B if Block A moves downward with velocity u? Advanced Problems A point traversed half the distance with velocity V0. The remaining part of the distance was covered with velocity V1 for half the time and the remaining half with velocity V2. Find the average velocity of the point for the whole time of motion. (Ans: 2 V0 (V1 + V2)/ ( 2 V0 + V1 + V2) ) A car starts moving rectilinearly, first with acceleration W=5.0m/s2( Initial velocity is zero), then uniformly and finally decelerating at the same rate W to come to a stop. The total time of motion equals =25seconds. If the average velocity for the whole duration of motion equals = 72Km/hr find the duration the car moved uniformly. ( Ans :15 secs) The displacement vector for a particle varies with time as r=at(1-bt) where a is a constant and b is a positive factor. Find The velocity v and the acceleration w of the particle as a function of time. The time interval taken by the particle to return to the initial points and the distance covered during that time.