A. Car B stops at the same place. At a certain moment, car a starts at a constant acceleration of 2m / S ^ 2. After 2 seconds, car B starts at a constant acceleration of 4.5m/x ^ 2 in the same direction (1) How long does car B leave to catch up with car a? (2) Before car B overtakes car a, what is the maximum distance between the two cars? Draw a V-T image

A. Car B stops at the same place. At a certain moment, car a starts at a constant acceleration of 2m / S ^ 2. After 2 seconds, car B starts at a constant acceleration of 4.5m/x ^ 2 in the same direction (1) How long does car B leave to catch up with car a? (2) Before car B overtakes car a, what is the maximum distance between the two cars? Draw a V-T image

x1= 1/2a1(t+2)^2
x2 = 1/2a2t^2
x1=x2
1/2a1(t+2)^2 = 1/2a2t^2
a1(t+2)^2 = a2t^2
2(t+2)^2 = 4.5t^2
{(t+2)/t}^2 = 2.25
(t+2)/t = 1.5
0.5t=2
t=4
Car B overtakes car a in 4S
△x = x1-x2
= 1/2a1(t+2)^2 - 1/2a2t^2
= 1/2*2(t+2)^2 - 1/2*4.5t^2
= (t+2)^2 - 2.25t^2
= -1.25t^2+4t+4
= -1.25(t^2-3.2)+4
= -1.25(t-1.6)^2 + 3.2+4
= -1.25(t-1.6)^2 + 7.2
≤7.2
Before car B overtakes car a, the maximum distance between the two cars is 7.2m
V1 = A1 (T + 2) = 2T + 4, where t ≥ - 2
V2 = a2t = 4.5t, where t ≥ 0
V1-t image: it is a ray whose end point is (- 2,0), inclines to the upper right and intercepts 4 on the positive half axis of ordinate;
V 2-T image: a ray whose end point is at the origin (0,0), tilts to the right and passes (1,4.5)