When the object moves with damping, the law of motion is x = e ^ (- 2t) * sin (3T + π / 6), then when t = 0

V|t=0=(dx/dt)|t=0=[-2e^(-2t)*sin(3t+π/6)+3e^(-2t)*cos(3t+π/6)]|t=0=（3√3)/2-1=1.58(m/s)

When a particle moves in a straight line along the x-axis, the change of its coordinate position x with time t is x = - 3T & # 178; + 3T + 7, starting from the zero point
Find the average velocity in 2S
Instantaneous velocity at the end of 2S

【1】
When t = 1:
X(1)=7
When t = 2:
X(2)=5
Displacement in 2S: S = x (2) - x (1) = 5-7 = - 2
Average velocity in 2S: v = s / Δ t = - 2
【2】
V(t)＝X‘（t）＝－6t+3
V(2)=-6x2+3＝－9

When a particle moves along the x-axis, its position coordinates change with time as x = - 2T ^ 2-3T + 1, t is in seconds
In the first second, the displacement of the particle is 5 meters. Why?
The particle always moves in the negative direction of the x-axis. Why?
I preview it myself

You can look at this problem like this: first, let t = 0, and the position coordinate of the particle is 1m. In the positive direction, let t = 1s, and the position coordinate of the particle is - 4m, and the displacement is equal to the end position minus the initial position, so the displacement is - 5m
As for why you move in a negative direction, it's easy to know the velocity of an object if you've learned how to find derivatives
V = - 4t-3, which is always a number less than 0, so it goes in the negative direction. However, it doesn't matter if you haven't learned how to calculate the derivative. If you draw the curve of the position coordinate changing with time t, it's a quadratic curve. Take a look at the slope of the quadratic curve. If the slope is negative, it means that the velocity is negative, and it's moving in the negative direction;

If the coordinate X of a particle moving on the x-axis changes with time t as x = 3t2 + 2t-4, then its acceleration a= And T = 0 (x is in meters, T & nbsp; is in seconds)

According to x = v0t + 12at2 and x = 3t2 + 2t-4, we know a = 6m / S2. When t = 0, the speed is 2m / s. so the answer is: 6m / S2; 2m / s

When the object moves with damping, the law of motion is x = e ^ (- 2t) * sin (3T + π / 6), then when t = 0