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?)

Question

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?)

askIITIians Expert · Answer

Hi Pritish, Remember that at the point of maxima and minima, dy/dx = 0 and if d 2 y/dx 2 is -ve, then that value of x gives maxima and if, d 2 y/dx 2 = +ve, then it is minima. Given, x = 3t 2 - 2t 3 dx/dt = 6t - 6t 2 For maxima, or minima, dx/dt = 0 6t - 6t 2 = 0 t = t 2 t (t - 1) = 0 t = 0s & t = 1 sec Let us find d 2 x/dt 2 (d 2 x/dt 2 ) t=0 = 6 - 12t = 6 - 12 x 0 = 6+ve (d 2 x/dt 2 ) 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

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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?)

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?)

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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?)

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?)

1 Answers

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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?)