The position function x ( t ) of a particle moving along an x axis is x = 5.0 -

Question

The position function x(t) of a particle moving along an x axis is x = 5.0 - 8.0t2, with x in meters and t in seconds.

(a) At what time does the particle (momentarily) stop?
___s

(b) Where does the particle (momentarily) stop?
___m

(c) At what negative time does the particle pass through the origin?
___ s

(d) At what positive time does the particle pass through the origin?
___s
(e) Graph x versus t for the range -5 s to +5 s. (Do this on paper. Your instructor may ask you to turn in this work.)

(f) To shift the curve leftward on the graph, should we include the term -20t or the term +20t in x(t)?

-20t or 20t    

(g) Does that inclusion increase or decrease the value of x at which the particle momentarily stops?

Explanation / Answer

a) set dx/dy =0
so x'=-16.0t 0=-16.0t (since velocity will equal zero)
therefore t=0
b) sub in time = 0 into equation
x=5-8.0(0)^2
x=5

Therefore we can assume that the particle starts at the position 5m at t=0

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