The position of a particle moving along the x axis depends on the time according to equation x = 3t 2 -2t 3 At what time does the particle reach its maximum positive x position? And when does it reach minimum? (I believe this requires calculus. Could someone show me?)

Pritish Chakraborty Grade: 12

        The position of a particle moving along the x axis depends on the time according to equation x = 3t²-2t³

At what time does the particle reach its maximum positive x position? And when does it reach minimum?

(I believe this requires calculus. Could someone show me?)

9 years ago

Answers : (1)

askIITIians Expert

21 Points

										Hi Pritish,
Remember that at the point of maxima and minima, dy/dx = 0
and if d²y/dx² is -ve, then that value of x gives maxima and if,
d²y/dx² = +ve, then it is minima.
Given, x = 3t² - 2t³
dx/dt = 6t - 6t²
For maxima, or minima,
dx/dt = 0
6t - 6t²= 0
t = t²
t (t - 1) = 0
t = 0s & t = 1 sec
Let us find d²x/dt²
(d²x/dt²)_t=0₌6 - 12t      
                       =   6 - 12 x 0
                       =  6+ve
(d²x/dt²)_{t=1  =  6 - 12 x 1}


                       = -6 
                       =  - ve
Hence, at t = 1 sec, particle reaches its maximum +ve  x position and at x = 0 it reaches minimum x - position