Homework Sourse10 If Dx x 2cosx represents the distance traveled by a par
10. If D(x) = x + 2cosx represents the distance traveled by a particle from
x = 0 to x = 2 . Find an x value in (0, 2 ) for which the instantaneous
velocity equals the average velocity.
x = 0 to x = 2 . Find an x value in (0, 2 ) for which the instantaneous
velocity equals the average velocity.
Solution
You have already obtained for the instantaneous velocity ( I will plug in values for a and b at the end): v(t) = dx/dt = 3 b t² - 2 c t The average velocity over a time t is: the distance covered in time t, divided by time t ! v_avg(t) = x(t) / t = b t² - c t Equating these gives: 3 b t² - 2 c t = b t² - c t 2 b t² - c t = 0 t = 0 or 2 b t - c = 0 The other than t=0 solution thus is t = c/(2b) = 3.6 m/s² / ( 8.4 m/s³ ) = 0.43 s
