omework: 3.4 HW Score: 88 9 of 12 (12 complete) ore: 022 of 1 pt 3.4.18 The acco

Question

omework: 3.4 HW Score: 88 9 of 12 (12 complete) ore: 022 of 1 pt 3.4.18 The accompanying figure shows the velocity v f(t) of a particle moving on a coordinate line. (a) When does the particle move forward? move backward? speed up? slow down? b) When is the particle's acceleration positive? negative? zero? (c) When does the particle move at its greatest speed? (d) When does the particle stand still for more than an instant? t (sec) 8 9-10 Type an equation or a compound inequality, Type an expression using t as the variable. Use a comma to separate answers as needed

Explanation / Answer

displacement is the area of the chart between velocity and time

acceleration is the slope of the tangent at curve at any point

(a)

Particle move forward when displacement is positive. so answer is (0,3) U (5,8)

Particle move backward when displacement is negative. so answer is (3,5)

Speed up when acceleration is positive: slope of the line is positive when x is 0 to 1 and then x = 5 to 6

so answer is (0,1) U (4,6)

Slow down when acceleration is negative: slope of the line is negative when x is 2 to 4 and then x = 6 to 8

so answer is (2,4) U (6,8)

(b)

Acceleration is positive on (0,1) U (4,6) when speed is increasing

Acceleration is positive on (2,4) U (6,8) when speed is increasing

(c)

greatest speed is at t = 1 to t = 2 and t = 6

so answer is [1,2] U {6}

(d)

Stand still is when velocity is 0 so the displacement will be 0 and so does the chart area.

answer is x = 3, 5, and [8,10]

so x = [8,10] U {3,5}

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