Chapter 2.
Motion Along a Straight Line
Myung-Hwa Jung (Sogang University)
Position & Displacement
Position : x1, x2
Displacement (vector) :
Dx = x2 - x1
1
Average Velocity vs. Speed
vavg =
Dx x2 - x1
=
(vector)
Dt t 2 - t1
(scalar)
Instantaneous Velocity
Average velocity
vavg =
x2 - x1 Dx
=
t 2 - t1 Dt
Instantaneous velocity
Dx dx
=
Dt ® 0 Dt
dt
v = lim
2
Average & Instantaneous Acceleration
Average acceleration
aavg =
v2 - v1 Dv
=
t 2 - t1 Dt
Instantaneous acceleration
Dv dv
=
Dt ®0 Dt
dt
d æ dx ö d 2 x
= ç ÷= 2
dt è dt ø dt
a = lim
Constant Acceleration
a = aavg =
v - v0
t -0
Þ v = v0 + at
where v0 : velocity at t = 0
vavg =
Þ
x - x0
,
t -0
vavg =
v + v0
2
x - x0 = 12 (v + v0 )t
where x0 : position at t = 0
3
등가속도 운동
x - x0 = 12 (v + v0 )t
v = v0 + at
t=
v - v0
a
v 2 - v02 = 2a ( x - x0 )
Þ
v = v0 + at Þ
x - x0 = v0t + 12 at 2
v0 = v - at Þ
x - x0 = vt - 12 at 2
Equations for Motion with Constant Acceleration
운동 방정식
v = v0 + at
모르는 양
x - x0
x - x0 = v0t + 12 at 2
v
v 2 - v02 = 2a ( x - x0 )
t
x - x0 = 12 (v0 + v)t
a
x - x0 = vt - 12 at 2
v0
4
Graphical Integration in Motion Analysis
t1
v1 - v0 = ò adt
t0
t1
x1 - x0 = ò vdt
t0
Summary
• 보기문제
: 2.01, 2.03, 2.05
• 연습문제
5