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The position of a particle moving along the x axis depends on the time according to...

The position of a particle moving along the x axis depends on the time according to the equation x = ct2 − bt3, where x is in meters and t in seconds.

For the following, let the numerical values of c and b be 5.1 and 1.5, respectively. (For vector quantities, indicate direction with the sign of your answer.)

(c) At what time does the particle reach its maximum positive x position? From t = 0.0 s to t = 4.0 s, what distance does the particle move?
(e) From t = 0.0 s to t = 4.0 s, what is its displacement?

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Answer #1

(c) Maximum positive x position reaches at t = 1.505 s.

Distance travelled between t=0, t=4s is D = 27.22 m.

(e.) Maximum displacement = 14.4 m. ( in -x direction)

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