The position of a particlemoving along the x axis depends on the time according

Question

The position of a particlemoving along the x axis depends on the time according to theequation x=ct2- bt3, where x is in meter antt in seconds. what are the units of (a) constant c and (b) constant b? Let their numerical values be 3.0 and 2.0,respectively. (c) At what time does the particle reach it maximumpositive x position? From t= 0.0s to t= 4.0s, (d) what distancedoes the particle move and (e) what is its displacement? find itsvelocity at times (f) 1.0s, (g) 2.0s, (h)3.0s, and (i) 4.0s. Findits acceleration at times (j) 1.0s, (k) 2.0s, (l) 3.0s and (m)4.0s.

Explanation / Answer

x = c t2 - b t3 v = dx / dt = 2 c t - 3 b t2 a = dv / dt = 2 c - 6 bt         use the last 2equations to answer f thru m At t = 0 v = 0 When v = 0 (the maximum displacement) 2 c t = 3 b t2 t = 2 c / (3 b) = 6 / 6 = 1 sec (after this time theparticle reverses direction and continues in the negativex-direction Its maximum displacement is x = c - b = 1 After 4 sec    x = 3 * 16 - 2 * 64 =-80     (its displacement) So the particle has moved 1 + 1 + 80 = 82 t = 2 c / (3 b) = 6 / 6 = 1 sec (after this time theparticle reverses direction and continues in the negativex-direction Its maximum displacement is x = c - b = 1 After 4 sec    x = 3 * 16 - 2 * 64 =-80     (its displacement) So the particle has moved 1 + 1 + 80 = 82

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