Question

give an exmaple in which the distance traversed by a particle is larger than the magnitude of its displacement in the same time. ?

Answer 1

 Rest and Motion:If the position of an object does not change as time passes, it is said to be at rest. If itchanges as time passes, the object is said to be in motion.Describing position:The position of a particle is described by giving (a) its distance from a fixed pointcalled the origin, and (b) its direction as seen from the origin. The position of a particle moving along astraight line is described by a quantity x. The numerical value of x gives the distance of the particle from theorigin, and its sign indicates whether the particle is in the positive direction or in the negative direction asseen from the origin.Displacement:The change in the position of a particle during a time interval is called its displacement inthat time interval. The displacement tells us two things: (a) how far the final position is from the initialposition, and (b) in which direction the final position is as seen from the initial position.Scalar quantities:A quantity that has a magnitude and follows the usual arithmetic rules of addition iscalled a scalar quantity.Vector quantities:A quantity that has a magnitude and a direction and follows the same rules of addition asdisplacements do is called a vector quantity.Average speed:average speed = Total distance travelled/ total time interval.Speed:The speed of an object is equal to the distance traversed by it in a very short time interval divided bythe time interval. It is a scaler quantity and its S.I. unit is m/s.Uniform speed:If an object covers equal distances in equal time intervals, it is said to move with a uniformor constant speed.Velocity:The velocity of an object is a quantity that gives the speed of the object as well as the direction of its motion. Velocity changes if either speed or the direction of motion changes. It is a vector quantity and itsS.I. unit is m/s.Acceleration:(a) The acceleration of an object is equal to the change in its velocity per unit time. (b) If thevelocity of an object changes by equal amounts in equal time intervals, the object is said to have a uniformacceleration.Distance-time graph:(a) The distance-time graph of an object movig with a uniform speed is a straightline. Conversely, if the distance-time graph of an object is a straight line, the object is moving with auniform speed. (b)The slope of the distance-time graph of an object equals its speed.(c) If an objectmoves with nonuniform speed, its distance-time graph is not a straight line. The slope of the tangent at anypoint of the graph gives the speed at the corresponding time.Displacement-time graph:(a) The displacement-time graph of an object moving with a uniform velocity isa straight line. (b)The slope of the displacement-time graph of an object equals its velocity.(c) Thedisplacement-time graph for a uniformly accelerated object has a parabolic shape. Speed-time graph:(a) If an object moves with a constant speed, its speed-time graph is a straight lineparallel to the time-axis. (b) The area under the speed-time graph gives the distance traversed by the objectin the corresponding time interval.Velocity-time graph:(a) If an object moves with a constant acceleration in a straight line, its velocitytimegraph is a straight line. (b) The slope of the velocity-time graph gives the acceleration of the object.(c) The area under a velocity-time graph gives the displacement of the object.Circular motion:A particle moving in a circular path changes its direction continuously and hence isaccelerated.Mathematical equationsS = vt s = distance, v = speed (assumed constant), t = timeV = u + at u = velocity at t = 0, v = velocity at time t, a = acceleration (assumed constant)s = ut + (at2)/2 at s displacement during time 0 to t, u velocity at t = 0, a = acceleration (assumed constant)v2= u2+ 2as symbols have the same meaning as in the above equations