A particle\'s position is given by x = 12.0 - 9.00t + 3t2, in which x is in mete

Question

A particle's position is given by x = 12.0 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer "0". (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer "0".

Explanation / Answer

A particle's position is given by x = 12.0 - 9.00t + 3t2, in which x is in meters and t is in seconds.

(a) What is its velocity at t = 1 s?
V = -9.00+3*1 = -6 m/sec

(b) Is it moving in the positive or negative direction of x just then?
it is moving in the positive direction of x

(c) What is its speed just then?
Speed = -9+3t

(d) Is the speed increasing or decreasing just then?
speed VS time is increasing

(Try answering the next two questions without further calculation.)
(e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer "0".
when t = ?3, then 3*t^2 = 9 which equates -9 and then speed is zero
(f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer "0".
no (0)

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