【公式】匀变速直线运动


1、匀速直线运动:

(1)速度:\(v=\dfrac{x}{t}\)

(2)位移:\(s=vt\)


2、匀变速直线运动:

(1)速度与时间关系:

\(v_{t}=v_{0}+at\)

(2)位移与时间关系:

\(x=v_{0}t+\dfrac{1}{2}at^{2}\)

(3)位移与速度关系:

\(v_{t}^{2}-v_{0}^{2}=2ax\)

(4)中间时刻速度:

\(v_{\frac{t}{2}}=\bar{v}=\dfrac{x}{t}=\dfrac{v_{0}+v_{t}}{2}\)

(5)位移中点速度:

\(v_{\frac{x}{2}}=\sqrt{\dfrac{v_{0}^{2}+v_{t}^{2}}{2}}\)

(6)匀速直线运动时:

\(v_{\frac{x}{2}}=v_{\frac{t}{2}}\)

(7)匀加速或匀减速直线运动时:

\(v_{\frac{x}{2}}>v_{\frac{t}{2}}\)


3、初速为零的匀加速直线运动,\(t_{1}=T,t_{2}=2T,t_{3}=3T,\cdots ,t_{n}=nT\)

 

(1)\(t_{1},t_{2},t_{3},\cdots ,t_{n}\)末瞬时速度比\(v_{1}:v_{2}:v_{3}:\cdots :v_{n}=1:2:3:\cdots :n\)

 

(2)在\(t_{1},t_{2},t_{3},\cdots ,t_{n}\)内位移比\(x_{1}:x_{2}:x_{3}:\cdots :x_{n}=1^{2}:2^{2}:3^{2}:\cdots :n^{2}\)

 

(3)第1个T内、第 2个T内、第3个T内……第n个T内位移之比为\(s_{1}:s_{2}:s_{3}:\cdots :s_{n}=\)\(1:3:5:\cdots :(2n-1)\)

 

(4)通过连续相等位移的时间比为\(t_{1}:t_{2}:t_{3}:\cdots :t_{n}=1:(\sqrt{2}-1):\)\((\sqrt{3}-\sqrt{2}):\cdots :(\sqrt{n}-\sqrt{n-1})\)


4、等时间隔与位移差:

(1)相邻等时间隔位移差为定值:

\(\Delta s=aT^{2}\)