# Example 2-1
t = 3 s
x1 = 50 m
x2 = 30.5 m
v = (x2 - x1) / t

# Example 2-2
t = 2.5 hr
v = 18 kph
x = v * t; km

# Example 2-3
a = 2.10 m / s^2
b = 2.80 m
t1 = 3 s
x1 = a * t1^2 + b
t2 = 5 s
x2 = a * t2^2 + b
del_x = x2 - x1
v = del_x / (t2 - t1)
v2 = 2 * a * t2

# Example 2-4
v1 = 0 kph
v2 = 90 kph
t1 = 0 s
t2 = 5 s
a = (v2 - v1) / (t2 - t1)

# Example 2-6
v1 = 15 m/s
t = 5s
v2 = 5 m/s
a = (v2 - v1) / t

# Example 2-7
a = 2.10 m / s^2
b = 2.80 m
t1 = 3 s
x1 = a * t1^2 + b
v1 = 2 * a * t1
t2 = 5 s
x2 = a * t2^2 + b
v2 = 2 * a * t2
a_bar = (v2 - v1) / (t2 - t1)
a_exact = 2 * a

# Example 2-9
v0 = 100 kph
a = 2 m/s^2
x = 150 m
v = sqrt(2 * a * x)
min_del_x = (v0^2) / (2 * a)

# Example 2-10
x = 30 m
a = 2 m / s^2
t = sqrt(2 * x / a)

# Example 2-11
v = 100 kph
x = 1 m
a = -(v^2) / (2 * x)
t = (-v) / a

# Example 2-12
v0 = 14 m/s
t = 0.5 s
x1 = v0 * t
v2 = 0 m/ s
a = -6 m/s^2
x2 = x1 + (v2^2 - v0^2) / (2 * a)

# Example 2-13
v= 100 kph
t = 5 s
ap = v / t
v0s = 150 kph
BEGIN
   t1 = 20 s
   xs = v0s * t1
   xp = 0.5 * ap * t1^2
   eq = xs - xp
END
solve(eq, t1)
vp = ap * t1

# Example 2-14
a = 9.8 m/s^2
t1 = 1 s
y1 = 0.5 * a * t1^2
t2 = 2 s
y2 = 0.5 * a * t2^2
t3 = 3 s
y3 = 0.5 * a * t3^2

# Example 2-15
a = 9.8 m/s^2
v0 = 3 m / s
t = 1 s
y = v0 * t + (1/2) * a * t^2
t = 2 s
y = v0 * t + (1/2) * a * t^2

v0 = 0 m / s
t = 1 s
y = v0 * t + (1/2) * a * t^2
t = 2 s
y = v0 * t + (1/2) * a * t^2

# Example 2-16
v = 0 m/s
v0 = 15 m/s
a = -9.8 m/s^2
y = (v^2 - v0^2) / (2 * a)
BEGIN
   y0 = 0 m
   t = 10 s
   y = y0 + v0 * t + 0.5 * a * t^2
END
solve(y,t)

# Example 2-18
v0 = 15.0 m/s
a = -9.8 m/s^2
t = -v0 / a
t2 = 3.06 s
v = v0 + a * t2

# Example 2-19
y = 8 m
y0 = 0 m
v0 = 15 m/s
a = -9.8 m/s^2
BEGIN
   t = 1 s
   eq = y - (y0 + v0 * t + 0.5 * a * t^2)
END
t = 1 s
solve(eq, t)
t = 3 s
solve(eq,t)

# Example 2-20
a = -9.8 m/s^2
v0 = 15 m/s
y0 = 0 m
y = -50 m
BEGIN
  t = 1 s
  eq = y - (y0 + v0 * t + 0.5 * a * t^2)
END
t = 1 s
solve(eq,t)
t = 10 s
solve(eq,t)

# Example 2-21
t = 2 s
b = 7.0 m/s^3
v = b * t^2 / 2
x = b * t^3 / 6

# Example 2-22
a1 = 0.5 m/s^2
a2 = 4.5 m/s^2
a3 = 12.5 m/s^2
a4 = 24.5 m/s^2
del_t = 0.5 s
v = (a1 + a2 + a3 + a4)* del_t
a1 = 0.08 m/s^2
a2 = 0.72  m/s^2
a3 = 2.00 m/s^2
a4 = 3.92 m/s^2
a5 = 6.48 m/s^2
a6 = 9.68 m/s^2
a7 = 13.52 m/s^2
a8 = 18.00 m/s^2
a9 = 23.12 m/s^2
a10 = 28.88 m/s^2
del_t = 0.2 s
v = (a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10)* del_t

# Homework Problems:

TBD