The following graphs show position as a function oftime for a particle that move
ID: 1735391 • Letter: T
Question
The following graphs show position as a function oftime for a particle that moves along the x axis. Selectthegraphs that at t = 1 s (the vertical hash mark across thex-axis is one second), fit the following situations.
(a) zero velocity and positive acceleration
(b) zero velocity and negative acceleration
(c) negative velocity and positive acceleration
(d) negative velocity and negativeacceleration.
(e) In which graph(s) would the speed of theparticle be increasing and not zero at t = 1 s?
I will grant lifesaver for a somewhat detailedexplanation for the reasoning behind the answers. Its been awhilesince I've dealt with the graphs of p(t), v(t) and a(t)..
Explanation / Answer
PART a>>>> zero velocitymeans that the slope of the tangent line at t=1 is zero (ie,tangent line is horizontal) on x vs t graph. Positive acceleration means 2nd derivative of xs is positive, whichmeans graph of x vs t at t=t is concave upward. The only graph with a flat tangent line and concave up at t=1is GRAPH 1. PART b>>> We are looking for a horizontaltangent line and concave down >>>> GRAPH 2. PART c>>> Negative velocity means theslope of the tangent line at t=1 is negative; thus looking for negative slope and concave up >>>> GRAPH 6. PART d>>>> negative slope and concavedown >>>> GRAPH 4. PART e>>>>> note that problem says"speed" and not velocity. Speed is increasingwhen slope is + and graph is concave up OR slope is negative and graph is concavedown. There appears to be no + slope and concaveup, but GRAPH 4 is negative slope and concave down. Speed is increasing in negative direction.Related Questions
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