![]() If the velocities are v1 and v2 at times t1 and t2 respectively, then When the acceleration is plotted as a function of time, it is acceleration – time graph (Fig. The area under the v – t curve, between the given intervals of time, gives the change in displacement or the distance travelled by the particle during the same interval. If the displacements are s1 and s2 in times t1 and t2, then When the velocity of the particle is plotted as a function of time, it is velocity-time graph.Īs a = dv/dt, the slope of the v – t curve at any instant gives the acceleration of the particle (Fig. below the particle at time t1, has a positive velocity, at time t2, has zero velocity and at time t3, has negative velocity. When the displacement of the particle is plotted as a function of time, it is displacement – time graph. As v = ds/dt, the slope of the s – t graph at any instant gives the velocity of the particle at that instant. acceleration – time graph (a – t graph).displacement – time graph (s – t graph).Line graphs are used to show the relation of one quantity say displacement or velocity with another quantity such as time. If the displacement, velocity and acceleration of a particle are plotted with respect to time, they are known as, The graphs provide a convenient method to present pictorially, the basic informations about a variety of events. The negative acceleration is called retardation or deceleration.Ī particle is in uniform motion when it moves with constant velocity (i.e) zero acceleration. If the velocity decreases with time, the acceleration is negative. ![]() ![]() If the velocity changes by an equal amount in equal intervals of time, however small these intervals of time may be, the acceleration is said to be uniform. Its unit is m s−2 and its dimensional formula is LT−2. The instantaneous acceleration is, a= dv/dt = d/dt =(ds/dt)=d2s/dt2 If u is the initial velocity and v, the final velocity of the particle after a time t, then the acceleration, Acceleration is a vector quantity.Īcceleration = change in velocity/time taken If the magnitude or the direction or both of the velocity changes with respect to time, the particle is said to be under acceleration. Acceleration of a particle is defined as the rate of change of velocity. It is the velocity at any given instant of time or at any given point of its path. Vaverage = change in displacement / change in timeįrom the graph, it is found that the slope of the curve varies. The average velocity during the time interval (t2 – t1) is defined as Let s1 be the displacement of a body in time t1 and s2 be its displacement in time t2 (Fig.below). The velocity is variable (non-uniform), if it covers unequal displacements in equal intervals of time or if the direction of motion changes or if both the rate of motion and the direction change. below) the slope is constant at all the points, when the particle moves with uniform velocity. Its unit is m s−1 and its dimensional formula is LT−1.Ī particle is said to move with uniform velocity if it moves along a fixed direction and covers equal displacements in equal intervals of time, however small these intervals of time may be. In a displacement – time graph, (Fig. It is also defined as the speed of the particle in a given direction. The velocity of a particle is defined as the rate of change of displacement of the particle. It is the distance travelled in unit time. The distance travelled is a scalar quantity and the displacement is a vector quantity. ![]() For example, if the particle moves from a point O to position P1 and then to position P2, its displacement at the position P2 is – x2 from the origin but, the distance travelled by the particle is x1+x1+x2 = (2×1+x2) (Fig below). The distance travelled by a particle, however, is different from its displacement from the origin. The motion of a particle can be described if its position is known continuously with respect to time. The total length of the path is the distance travelled by the particle and the shortest distance between the initial and final position of the particle is the displacement. Position, displacement and distance travelled by the particle The important parameters required to study the motion along a straight line are position, displacement, velocity, and acceleration. The motion along a straight line is known as rectilinear motion. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |