The graph is of right is of the motion of two children, Ariel and Byron, who are

Question

The graph is of right is of the motion of two children, Ariel and Byron, who are moving along a straight hallway. The vertical axis is not labeled. If the vertical axis is position, does either child ever change direction? If so, at what time does this change in direction occur? Explain If the vertical axis is position are the two children ever at the same position along the hallway? If so, at what time or times? Explain. If the vertical axis is position, do the two children ever have the same speed? If so, at what time or times? Explain. If the vertical axis is position do the two children ever have the same acceleration? If so, at what time or times? Explain. If the vertical axis is velocity, do either or the children ever change direction? If so, at what time or times does this change in direction occur? Explain. If the vertical axis is velocity, do the two children ever have the same velocity? If so, at what time or times? Explain. If the vertical axis is velocity, do the two children ever have the same acceleration? If so, at what time or times? Explain.

Explanation / Answer

ANSWERED THE FIRTS FOUR SUBPARTS OF THE QUESTION, if you'd like more help please submit the other subparts in another question

a) No, both children are going in the positive side of the vertical axis direction, from the graphics we can tell that they move at different rates (ariel in a linear movement and byron in a cuadratic movement).

b) Yes, at the time when both graphics intersect, that is in t=2s and t=8s.

c) We'll need the equations of both curves, Ariel's equation is y=3/5x-3 and byron's y=kx2-2; we'll need to calculate the value of k, for that we evaluate the linear equation in x=2 (intersection point), it yields y=-9/5, then we evaluate the point (x,y)=(2,-9/5) in the cuadratic eq, thus we have: -9/5=4k-2 solving for k yields a value of 1/20, the equation for byron is y=1/20x2-2

after that we derivate both equations so we know how is the speed of both children, the derivate of ariel's is 3/5 while the derivate of byron's is 1/10x, then for the time when both have the same speed will be 3/5=1/10x, solving for x gives us x=6s or t=6s.

d) No, ariels is movimg at a constant speed since dv/dt=0, while Byron is moving at a constant acceleration of 0.1 m/s2.

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