Physics

Motion in a straight line 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. 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. 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. Motion in a plane Two bodies were thrown simultaneously from the same point, one straight up and other at an angle of 60 degrees with horizontal. The initial velocity of each body Is V=25m/s . Find the distance between the two bodies at t=1.70 seconds. A balloon starts rising from the surface of the earth. The ascension rate is constant equal to V0. Due to wind the balloon gathers a horizontal velocity component equal to Vx=ay where a is a constant and y is the height of ascent. Find Horizontal drift of balloon as x(y) The total acceleration of the balloon. A ball starts falling with zero initial velocity towards an incline plane forming an angle with horizontal. After falling a distance h, the ball rebounds elastically off the inclined plane. Find the distance from the point of impact the ball will rebound for the second time on the incline. Relativistic Motion Two swimmers leave point Aon one bank of the river to reach point B directly on opposite side of the river bank. One of them crosses along the straight line AB while the other swims at right angles to the direction of the stream and then walks the distance that he has been carried away by the stream to get to the point B. What was the velocity of his walking if both swimmers reached the destination simultaneously? An elevator car whose floor to ceiling distance is L=2.7m starts ascending with acceleration a=1.2m/s2. After t=2 sec a bolt starts falling from the ceiling of the car. Find a)the bolt’s free fall time b) the displacement and the distance in the reference frame fixed to ground.