If a particle\'s position is given by x=4-12t+3t 2 ( wheret is in seconds and x

Question

If a particle's position is given by x=4-12t+3t2( wheret is in seconds and x is in meters), what is its velocity att=1s?(b) Is it moving in the positive or negative direction of xjust then? (c) what is its speed just then? (d)Is the speedincreasing or decreasing just then?(Try answering the next twoquestions without further calculation.) (e) is there ever aninstant when the velocity is zero? If so, give the time t; if not,answer no. (f) Is there a time after t =3s when the particle ismoving in the negative direction of x? If so, give the time t; ifnot answer no.

Explanation / Answer

particle position             x = 4 - 12t +3t2 a) velocity of the particle              v = dx / dt               = d / dt ( 4 - 12t +3t2 )               = 6 t - 12    at t = 1 s        velocity of the particle v = 6 - 12   = - 6 m/s here negative sign represents opposite direction b) negative x - direction d) speed decreases   e) at t = 2s       velocity v = 6 (2) - 12 = 0 m/s f ) no

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