The number represented by point a on the number axis is 8, B is on the left side of a, and ab = 14. Starting from point a, the moving point P moves to the left along the number axis at the speed of 5 unit lengths per second, and the movement time is t (T > 0) seconds, The number represented by point P (expressed in an algebraic formula containing T) 2. The moving point Q starts from point B and advances to the left at a speed of 3 unit lengths per second along the number axis at a uniform speed. If point P and Q start at the same time, how many seconds does point P move to catch up with point q? 3. If M is the midpoint of AP and N is the midpoint of Pb, does the length of line Mn change during the movement of point P? If so, explain the reason personally. If not, please draw a graph, And find out the length of line Mn

The number represented by point a on the number axis is 8, B is on the left side of a, and ab = 14. Starting from point a, the moving point P moves to the left along the number axis at the speed of 5 unit lengths per second, and the movement time is t (T > 0) seconds, The number represented by point P (expressed in an algebraic formula containing T) 2. The moving point Q starts from point B and advances to the left at a speed of 3 unit lengths per second along the number axis at a uniform speed. If point P and Q start at the same time, how many seconds does point P move to catch up with point q? 3. If M is the midpoint of AP and N is the midpoint of Pb, does the length of line Mn change during the movement of point P? If so, explain the reason personally. If not, please draw a graph, And find out the length of line Mn

1. Taking the right direction of the number axis as the positive direction, let the number represented by the point B on the number axis be: X
The solution is: x = 8-14, x = - 4
Then: XP = 8-5t (XP is the coordinate of point P on the number axis)
2. The relative velocity of P and Q is v = - 5 - (- 3) = - 2 / s
The relative displacement of PQ is s = - 14
Let: catch up time be: T
Then s = VT, t = 14 / 2 = 7S
3. XM = 8-5t / 2 (XM is the coordinate of m point on the number axis)
Xn = - 6 + (14-5t) / 2 (xn is the coordinate of N point on the number axis)
Mn = xn XM = - 6 + (14-5t) / 2-8 + 5t / 2 = - 6 + 7-5t / 2-8 + 5t / 2 = - 7. A negative sign indicates the opposite direction
The length of Mn is always 7 units