We can now calculate the displacement as a function of time x t (6) The velocity also can be given as a function of v x (7) straight line graphs When = 0 the stopping distance is v We can now investigate what happens when The object keeps moving till = 0, which happens only in the limit . Then the v object stop at the position . We can define a time constant The velocity and displacement can be expressed as After a time of about 5, the particle will stop when the speed of the particle becomes zero stopping time ~ 5 The stopping time is independent of the initial velocity but the greater the initial velocity the greater the stopping distance. The larger the constant , the shorter the stopping distance and quicker it stops and the larger the mass, the greater the stopping distance and it takes a longer time to stop the object. Numerical Approach We can also find the velocity and displacement of the object by solving Newton’s Second Law of motion using a finite difference method.
We can now calculate the displacement x as a function of time t (6) The velocity v also can be given as a function of x (7) straight line graphs When v = 0 the stopping distance is We can now investigate what happens when The object keeps moving till v = 0, which happens only in the limit . Then the object stop at the position . We can define a time constant The velocity and displacement can be expressed as After a time of about 5, the particle will stop when the speed of the particle becomes zero stopping time ~ 5 The stopping time is independent of the initial velocity but the greater the initial velocity the greater the stopping distance. The larger the constant , the shorter the stopping distance and quicker it stops and the larger the mass, the greater the stopping distance and it takes a longer time to stop the object. Numerical Approach We can also find the velocity and displacement of the object by solving Newton’s Second Law of motion using a finite difference method.