Example 2

Average and instantaneous velocities .

A Mass m1 located in 20 m to the east of an observer. At time t= 0 the mass m1 move to the mass m2 in a clearing 50 east of the observer. The mass m1 runs along a straight line; later analysis of a videotape shows that during the first 2.0 s of the attack, the mass m1 is coordinate x varies with time according to the equation x = 20 m+(50m/s^2)t^2.



a) Find the displacement of the mass m1 during the interval between t1 =1.0 s and t2 = 2.0 s


Solution

At time t1 = 1.0 s the mass m1 is position x1 is

x1 = 20 m + (5.0 m/s^2)(1.0s)^2 = 25 m.


At time t2= 2.0 s its position x2 is
x2 = 20 m + (5.0 m/s^2)(2.0s)^2 = 40 m.


The displacement during this intervals is

Delta x = x2-x1 = 40 m – 25 m = 15 m.


Answer

b) Find the average velocity during the same time interval.


vav = (x2-x1)/(t2-t1)=(40m-25m)/(2.0s-1.0s) = 15 m/1.0s =15 m/s

Answer

c) Find the instantaneous velocity at time t1 = 1.0 s by takeing first detta t = 0.1 s, then delta t = 0.01 s, then delta t= 0.001 s.


Next : Find the instantaneous velocity (cont.1)