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this is a one page assignment. I just want to see how you do, so I can assign my quizzes. They grade a special way. I will pay for this to see.

Net Change Theorem & Particle Motion Unit 6 Class #9 #3: / (hours) 0 Vp(t ) I (meters per hour) 0 0.3 1.7 2.8 4 55 - 29 55 48 The velocity of a particle P, moving along the x-axis is given by the differentiable function vp, where vp(t) is measured in meters per hour and tis measured in hours. Selected values of vp(t) are shown in the table above. Particle Pis at the origin at time t = 0. (a) Justify why there must be at least one time t, for 0.3 :5 t :5 2.8 at which v;(t), the acceleration of particle P, equals 0 meters per hour per hour. (b) Using a trapezoidal sum with the three subintervals [0,0.3], [0.3,1.7], and [1.7,2.8] to approximate the value of fo2 .s vp(t) dt. (c) A second particle Q, also moves along the x -axis so that its velocity for 0 :5 t :5 4 is given by vQ(t) = 45../t cos(0.063t2) meters per hour. Find the time interval during which the velocity of particle Q is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is atleast 60 meters per hour. (d) At time t = 0, particle Q is at position x = -90. Using the result from part (b) and the function vQ from part (c), approximate the distance between particles P and Q at time t = 2.8.

now-scan-may-15-2022-4kxvno1a-dnetkpmp.pdf

Answered Same DayMay 17, 2022

Answer To: this is a one page assignment. I just want to see how you do, so I can assign my quizzes. They grade...

Sudarshan K answered on May 18 2022

93 Votes

Advanced Mathematics
Background:
The velocity of particle P moving along x-axis (one dimensional motion), given by velocity function νp(t). This is velocity function dependant upon time.
Particle is at origin at time 0.
    T (hours)
    0
    0.3
    1.7
    2.8
    4
    νp(t).
    0
    55
    -29
    55
    48
This is velocity time graph. Differentiation of the curve made by above graph, will give acceleration. And taking integration of the above graph will give distance.

Question a:
Justify why there must be at least one time t, for which 0.3Solution:
The above solution depends upon the understanding the differentiation of the graph gives the slope of the curve at various points. For the acceleration to be zero, means the slope of the curve has to be zero or in other words, the tangent line drawn to curve at that point will be parallel to x axis.
Slope of the line follows the graph and as shown in the graph, at 0.3 and 2.8 the value is positive and at same height, whereas a point in between 1.7, the value is negative, which shows that curve bend from 0.3 to 2.8 going from positive to negative and back to positive.
Now using mean value theorem or rolle’s theorem for any continuous function between [a,b] such that f(a)=f(b), where a and b are real numbers, then there exists a point c in (a,b) such that f’(c)=0.
Using the same principle above, one can clearly...

SOLUTION.PDF

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