等速/等加速直線運動

等加速直線運動

v=v0+at
s=v0 t+1/2a t^2
v^2=v0^2+2as

ggb code

n=6

t=Slider(0,n)

eq1:y=v0+ a t
eq2:x=t

Intersect(eq1,eq2)
setTrace(A,true)
StartAnimation(t)

eq3:y=v0 t+1/2 a t^2

Intersect(eq2,eq3)
setTrace(B,true)
StartAnimation(t)

============================
一次輸入ggb code

Execute{(
"n=6",
"t=Slider(0,n)",
"eq1:y=v0+ a t",
"eq2:x=t",
"Intersect(eq1,eq2)",
"setTrace(A,true)",
"setColor(A,blue)",
"StartAnimation(t)",
"eq3:y=v0 t+1/2 a t^2",
"Intersect(eq2,eq3)",
"setTrace(B,true)",
"setColor(B,red)",
"StartAnimation(t)")}

等速直線運動(a=0 等加速直線運動)

v=v0
s=v0 t

the same ggb code

a=0


斜拋運動

vx=v0 cos(th)
vy=v0 sin(th)

y=vy t-1/2 g t^2
x=vx t

v0最小值
y=v0 sin(th) t-1/2gt^2>0
v0sin(th)t>1/2gt^2
v0>1/(2 sin(th))gt
    =1/2gt
    =4.9t

落地時間
t=(2 v0 sin(th))/g

最大高度
h=(v0 sin(th))^2/g

水平位移
x=(v0 sin(2 th))/g



th1=pi/6
th2=pi/4
th3=pi/3
g=9.8

t=10
v0=10

nn(th)=2 v0 sin(th)/g
th=th2
n=nn(th)
t=Slider(0,n)

eq1:y=v0 sin(th1) t-1/2 g t^2
eq2:y=v0 sin(th2) t-1/2 g t^2
eq3:y=v0 sin(th3) t-1/2 g t^2 
eq1x:x=v0 cos(th1) t
eq2x:x=v0 cos(th2) t
eq3x:x=v0 cos(th3) t

Intersect(eq1,eq1x)
Intersect(eq2,eq2x)
Intersect(eq3,eq3x)
 
setTrace(A,true)
setTrace(B,true)
setTrace(C,true) 
 
StartAnimation(t)


==============================
一次輸入ggb code

Execute({"th1=pi/6",
"th2=pi/4",
"th3=pi/3",
"g=9.8",
"v0=10",
"nn(th2)=2 v0 sin(th2)/g",
"n=nn(th2)",
"t=Slider(0,n)",
"eq1:y=v0 sin(th1) t-1/2 g t^2",
"eq2:y=v0 sin(th2) t-1/2 g t^2",
"eq3:y=v0 sin(th3) t-1/2 g t^2 ",
"eq1x:x=v0 cos(th1) t",
"eq2x:x=v0 cos(th2) t",
"eq3x:x=v0 cos(th3) t",
"Intersect(eq1,eq1x)",
"Intersect(eq2,eq2x)",
"Intersect(eq3,eq3x)",
"setTrace(A,true)",
"setTrace(B,true)",
"setTrace(C,true) ",
"StartAnimation(t)"})

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https://www.geogebra.org/m/ne6ug4jp